mihaibudiu commented on code in PR #4540: URL: https://github.com/apache/calcite/pull/4540#discussion_r2384259412
########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { Review Comment: an alternative approach is to actually count the number of basic operations you are doing in the loops below and once you exceed it return the approximation. ########## core/src/main/java/org/apache/calcite/rel/metadata/RelMdFunctionalDependency.java: ########## @@ -64,212 +78,353 @@ protected RelMdFunctionalDependency() {} return BuiltInMetadata.FunctionalDependency.DEF; } + /** + * Determines if column is functionally dependent on key for a given rel node. Review Comment: if this is a conservative approximation, please document if it is an over- or under- approximation, or if it is exact. I think this comments applies to many other methods in this class. ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,403 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { + return ImmutableBitSet.of(attributes); + } + + Set<Integer> closureSet = new HashSet<>(); + Queue<Integer> queue = new ArrayDeque<>(); + for (int attr : attributes) { + closureSet.add(attr); + queue.add(attr); + } + + Map<FunctionalDependency, Integer> fdMissingCount = new HashMap<>(); + Map<Integer, List<FunctionalDependency>> attrToFDs = new HashMap<>(); + for (FunctionalDependency fd : fdSet) { + fdMissingCount.put(fd, fd.getDeterminants().cardinality()); + for (int det : fd.getDeterminants()) { + attrToFDs.computeIfAbsent(det, k -> new ArrayList<>()).add(fd); + } + } + + while (!queue.isEmpty()) { + Integer attr = queue.poll(); + if (attr == null) { + continue; + } + List<FunctionalDependency> fds = attrToFDs.get(attr); + if (fds == null) { + continue; + } + for (FunctionalDependency fd : fds) { + Integer missing = fdMissingCount.get(fd); + if (missing == null) { + continue; + } + missing = missing - 1; + fdMissingCount.put(fd, missing); + if (missing == 0) { + for (int dep : fd.getDependents()) { + if (closureSet.add(dep)) { + queue.add(dep); + } + } + } + } + } + + return ImmutableBitSet.of(closureSet); + } + + /** + * Check if X determined Y is implied by this FD set. + */ + public boolean implies(ImmutableBitSet determinants, ImmutableBitSet dependents) { + return closure(determinants).contains(dependents); Review Comment: another idea would be to cache the closure once you have computed it, but this can be considered for a later PR, especially if measurements will show that the closure of a set of attributes is computed multiple times. ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { Review Comment: the fact that this can be an over-approximation should be documented in the JavaDoc ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { + return ImmutableBitSet.of(attributes); + } + + Set<Integer> closureSet = new HashSet<>(); + Queue<Integer> queue = new ArrayDeque<>(); + for (int attr : attributes) { + closureSet.add(attr); + queue.add(attr); + } + + Map<FunctionalDependency, Integer> fdMissingCount = new HashMap<>(); + Map<Integer, List<FunctionalDependency>> attrToFDs = new HashMap<>(); + for (FunctionalDependency fd : fdSet) { + fdMissingCount.put(fd, fd.getDeterminants().cardinality()); + for (int det : fd.getDeterminants()) { + attrToFDs.computeIfAbsent(det, k -> new ArrayList<>()).add(fd); + } + } + + while (!queue.isEmpty()) { + Integer attr = + requireNonNull(queue.poll(), "Queue returned null while computing closure"); + List<FunctionalDependency> fds = attrToFDs.get(attr); + if (fds == null) { + continue; + } + for (FunctionalDependency fd : fds) { + int missing = + requireNonNull(fdMissingCount.get(fd), "fdMissingCount returned null for FD " + fd); + missing = missing - 1; + fdMissingCount.put(fd, missing); + if (missing == 0) { + for (int dep : fd.getDependents()) { + if (closureSet.add(dep)) { + queue.add(dep); + } + } + } + } + } + + return ImmutableBitSet.of(closureSet); + } + + /** + * Check if X determined Y is implied by this FD set. + */ + public boolean implies(ImmutableBitSet determinants, ImmutableBitSet dependents) { + // Check if there is a direct FD match + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(determinants) + && fd.getDependents().contains(dependents)) { + return true; + } + } + return closure(determinants).contains(dependents); + } + + /** + * Check if a single column is functionally determined by another column. + */ + public boolean determines(int determinant, int dependent) { + // Check if there is a direct FD match + ImmutableBitSet detSet = ImmutableBitSet.of(determinant); + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(detSet) + && fd.getDependents().get(dependent)) { + return true; + } + } + return closure(detSet).get(dependent); + } + + /** + * Compute the minimal cover of this functional dependency set. + * Returns an equivalent set with minimal dependencies. + */ + public FunctionalDependencySet minimalCover() { + // Split multi-attribute right sides into single attributes + Set<FunctionalDependency> splitFDs = new HashSet<>(); + for (FunctionalDependency fd : fdSet) { + splitFDs.addAll(fd.split()); + } + splitFDs.removeIf(FunctionalDependency::isTrivial); + + // Remove redundant attributes from left sides + Set<FunctionalDependency> reducedFDs = new HashSet<>(); + for (FunctionalDependency fd : splitFDs) { + if (fd.getDeterminants().cardinality() <= 1) { + reducedFDs.add(fd); + } else { + FunctionalDependencySet tempSet = new FunctionalDependencySet(splitFDs); + tempSet.removeFD(fd); + reducedFDs.add(reduceLeft(fd, tempSet)); + } + } + + // Remove redundant functional dependencies + reducedFDs.removeIf(fd -> { + FunctionalDependencySet remainingFDs = new FunctionalDependencySet(reducedFDs); + remainingFDs.removeFD(fd); + return remainingFDs.implies(fd.getDeterminants(), fd.getDependents()); + }); + + return new FunctionalDependencySet(reducedFDs); + } + + /** + * Reduce left side by removing redundant columns from determinants. + */ + private static FunctionalDependency reduceLeft(FunctionalDependency fd, + FunctionalDependencySet fdSet) { + ImmutableBitSet determinants = fd.getDeterminants(); + ImmutableBitSet dependents = fd.getDependents(); + + // Try removing each attribute to find minimal determinant set + for (int attr : fd.getDeterminants()) { + ImmutableBitSet reduced = determinants.clear(attr); + if (fdSet.closure(reduced).contains(dependents)) { + determinants = reduced; + } + } + return FunctionalDependency.of(determinants, dependents); + } + + /** + * Check if this FD set is equivalent to another FD set. + * Two FD sets are equivalent if they have the same closure for any attribute set. Review Comment: the definition is fine, but the implementation seems to be different ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { + return ImmutableBitSet.of(attributes); + } + + Set<Integer> closureSet = new HashSet<>(); + Queue<Integer> queue = new ArrayDeque<>(); + for (int attr : attributes) { + closureSet.add(attr); + queue.add(attr); + } + + Map<FunctionalDependency, Integer> fdMissingCount = new HashMap<>(); + Map<Integer, List<FunctionalDependency>> attrToFDs = new HashMap<>(); + for (FunctionalDependency fd : fdSet) { + fdMissingCount.put(fd, fd.getDeterminants().cardinality()); + for (int det : fd.getDeterminants()) { + attrToFDs.computeIfAbsent(det, k -> new ArrayList<>()).add(fd); + } + } + + while (!queue.isEmpty()) { + Integer attr = + requireNonNull(queue.poll(), "Queue returned null while computing closure"); + List<FunctionalDependency> fds = attrToFDs.get(attr); + if (fds == null) { + continue; + } + for (FunctionalDependency fd : fds) { + int missing = + requireNonNull(fdMissingCount.get(fd), "fdMissingCount returned null for FD " + fd); + missing = missing - 1; + fdMissingCount.put(fd, missing); + if (missing == 0) { + for (int dep : fd.getDependents()) { + if (closureSet.add(dep)) { + queue.add(dep); + } + } + } + } + } + + return ImmutableBitSet.of(closureSet); + } + + /** + * Check if X determined Y is implied by this FD set. + */ + public boolean implies(ImmutableBitSet determinants, ImmutableBitSet dependents) { + // Check if there is a direct FD match + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(determinants) + && fd.getDependents().contains(dependents)) { + return true; + } + } + return closure(determinants).contains(dependents); + } + + /** + * Check if a single column is functionally determined by another column. + */ + public boolean determines(int determinant, int dependent) { + // Check if there is a direct FD match + ImmutableBitSet detSet = ImmutableBitSet.of(determinant); + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(detSet) + && fd.getDependents().get(dependent)) { + return true; + } + } + return closure(detSet).get(dependent); + } + + /** + * Compute the minimal cover of this functional dependency set. + * Returns an equivalent set with minimal dependencies. + */ + public FunctionalDependencySet minimalCover() { + // Split multi-attribute right sides into single attributes + Set<FunctionalDependency> splitFDs = new HashSet<>(); + for (FunctionalDependency fd : fdSet) { + splitFDs.addAll(fd.split()); + } + splitFDs.removeIf(FunctionalDependency::isTrivial); + + // Remove redundant attributes from left sides + Set<FunctionalDependency> reducedFDs = new HashSet<>(); + for (FunctionalDependency fd : splitFDs) { + if (fd.getDeterminants().cardinality() <= 1) { + reducedFDs.add(fd); + } else { + FunctionalDependencySet tempSet = new FunctionalDependencySet(splitFDs); + tempSet.removeFD(fd); + reducedFDs.add(reduceLeft(fd, tempSet)); + } + } + + // Remove redundant functional dependencies + reducedFDs.removeIf(fd -> { + FunctionalDependencySet remainingFDs = new FunctionalDependencySet(reducedFDs); + remainingFDs.removeFD(fd); + return remainingFDs.implies(fd.getDeterminants(), fd.getDependents()); + }); + + return new FunctionalDependencySet(reducedFDs); + } + + /** + * Reduce left side by removing redundant columns from determinants. + */ + private static FunctionalDependency reduceLeft(FunctionalDependency fd, + FunctionalDependencySet fdSet) { + ImmutableBitSet determinants = fd.getDeterminants(); + ImmutableBitSet dependents = fd.getDependents(); + + // Try removing each attribute to find minimal determinant set + for (int attr : fd.getDeterminants()) { + ImmutableBitSet reduced = determinants.clear(attr); + if (fdSet.closure(reduced).contains(dependents)) { + determinants = reduced; + } + } + return FunctionalDependency.of(determinants, dependents); + } + + /** + * Check if this FD set is equivalent to another FD set. + * Two FD sets are equivalent if they have the same closure for any attribute set. + */ + public boolean equalTo(FunctionalDependencySet other) { + for (FunctionalDependency fd : fdSet) { + if (!other.implies(fd.getDeterminants(), fd.getDependents())) { + return false; + } + } + + for (FunctionalDependency fd : other.fdSet) { + if (!implies(fd.getDeterminants(), fd.getDependents())) { + return false; + } + } + + return true; + } + + /** + * Find candidate keys within the given attribute set. + * + * @param attributes the set of attributes to search for candidate keys within + * @param onlyMinimalKeys if true, only return minimal candidate keys (shortest length); + * if false, return all minimal candidate keys + * @return a set of attribute subsets that can determine all given attributes + */ + public Set<ImmutableBitSet> findCandidateKeys( + ImmutableBitSet attributes, boolean onlyMinimalKeys) { + // Branch and bound algorithm for minimal candidate key search + if (fdSet.isEmpty()) { + return ImmutableSet.of(attributes); + } + + // Attributes that are not dependents of any FD + ImmutableBitSet essentialAttrs = findEssentialAttributes(attributes); + if (closure(essentialAttrs).contains(attributes)) { + return ImmutableSet.of(essentialAttrs); + } + + Set<ImmutableBitSet> result = new HashSet<>(); + int minKeySize = Integer.MAX_VALUE; + PriorityQueue<ImmutableBitSet> queue = + new PriorityQueue<>(Comparator.comparingInt(ImmutableBitSet::cardinality)); + Set<ImmutableBitSet> visited = new HashSet<>(); + queue.add(essentialAttrs); + + while (!queue.isEmpty()) { + ImmutableBitSet cand = + requireNonNull(queue.poll(), "Queue returned null while searching candidate keys"); + if (visited.contains(cand)) { + continue; + } + visited.add(cand); + if (onlyMinimalKeys && cand.cardinality() > minKeySize) { + break; + } + + // If a candidate key is a superset of key, It is a redundant set + boolean covered = false; + for (ImmutableBitSet key : result) { + if (cand.contains(key)) { + covered = true; + break; + } + } + + if (covered) { + continue; + } + + ImmutableBitSet candClosure = closure(cand); + if (candClosure.contains(attributes)) { + result.add(cand); + if (onlyMinimalKeys) { + minKeySize = cand.cardinality(); + } + continue; + } + + // Expand: only add attributes not in the closure + ImmutableBitSet remain = attributes.except(cand); + for (int attr : remain) { + if (candClosure.get(attr)) { + continue; + } + ImmutableBitSet next = cand.set(attr); + if (!visited.contains(next)) { + queue.add(next); + } + } + } + return result.isEmpty() ? ImmutableSet.of(attributes) : result; + } + + private ImmutableBitSet findEssentialAttributes(ImmutableBitSet attributes) { + // Find attributes that do not appear on the right side of any FD (essential for key) + ImmutableBitSet.Builder dependentsBuilder = ImmutableBitSet.builder(); + for (FunctionalDependency fd : fdSet) { + dependentsBuilder.addAll(fd.getDependents()); + } + ImmutableBitSet dependentsAttrs = dependentsBuilder.build(); + return attributes.except(dependentsAttrs); + } + + /** + * Computes the transitive closure of this FD set by repeatedly applying transitivity. + * For all {@code X->Y}, {@code Y->Z}, add {@code X->Z} until no new FDs are produced. + */ + public FunctionalDependencySet computeTransitiveClosure() { + boolean changed = true; + int loops = 0; + while (changed && loops++ < MAX_TRANSITIVE_CLOSURE_LOOPS) { Review Comment: what is the result if the loop count is exceeded? I expected it to be a conservative over-approximation of the transitive closure, but it seems to be an under-approximation. I guess the over-approximations are very large, but in other places where you approximate you tend to over-approximate. This behavior should be documented; and maybe even reflected in the function name "computeOrApproximateTransitiveClosure" ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { + return ImmutableBitSet.of(attributes); + } + + Set<Integer> closureSet = new HashSet<>(); + Queue<Integer> queue = new ArrayDeque<>(); + for (int attr : attributes) { + closureSet.add(attr); + queue.add(attr); + } + + Map<FunctionalDependency, Integer> fdMissingCount = new HashMap<>(); + Map<Integer, List<FunctionalDependency>> attrToFDs = new HashMap<>(); + for (FunctionalDependency fd : fdSet) { + fdMissingCount.put(fd, fd.getDeterminants().cardinality()); + for (int det : fd.getDeterminants()) { + attrToFDs.computeIfAbsent(det, k -> new ArrayList<>()).add(fd); + } + } + + while (!queue.isEmpty()) { + Integer attr = + requireNonNull(queue.poll(), "Queue returned null while computing closure"); + List<FunctionalDependency> fds = attrToFDs.get(attr); + if (fds == null) { + continue; + } + for (FunctionalDependency fd : fds) { + int missing = + requireNonNull(fdMissingCount.get(fd), "fdMissingCount returned null for FD " + fd); + missing = missing - 1; + fdMissingCount.put(fd, missing); + if (missing == 0) { + for (int dep : fd.getDependents()) { + if (closureSet.add(dep)) { + queue.add(dep); + } + } + } + } + } + + return ImmutableBitSet.of(closureSet); + } + + /** + * Check if X determined Y is implied by this FD set. + */ + public boolean implies(ImmutableBitSet determinants, ImmutableBitSet dependents) { + // Check if there is a direct FD match + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(determinants) + && fd.getDependents().contains(dependents)) { + return true; + } + } + return closure(determinants).contains(dependents); + } + + /** + * Check if a single column is functionally determined by another column. + */ + public boolean determines(int determinant, int dependent) { + // Check if there is a direct FD match + ImmutableBitSet detSet = ImmutableBitSet.of(determinant); + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(detSet) + && fd.getDependents().get(dependent)) { + return true; + } + } + return closure(detSet).get(dependent); + } + + /** + * Compute the minimal cover of this functional dependency set. + * Returns an equivalent set with minimal dependencies. + */ + public FunctionalDependencySet minimalCover() { + // Split multi-attribute right sides into single attributes + Set<FunctionalDependency> splitFDs = new HashSet<>(); + for (FunctionalDependency fd : fdSet) { + splitFDs.addAll(fd.split()); + } + splitFDs.removeIf(FunctionalDependency::isTrivial); + + // Remove redundant attributes from left sides + Set<FunctionalDependency> reducedFDs = new HashSet<>(); + for (FunctionalDependency fd : splitFDs) { + if (fd.getDeterminants().cardinality() <= 1) { + reducedFDs.add(fd); + } else { + FunctionalDependencySet tempSet = new FunctionalDependencySet(splitFDs); + tempSet.removeFD(fd); + reducedFDs.add(reduceLeft(fd, tempSet)); + } + } + + // Remove redundant functional dependencies + reducedFDs.removeIf(fd -> { + FunctionalDependencySet remainingFDs = new FunctionalDependencySet(reducedFDs); + remainingFDs.removeFD(fd); + return remainingFDs.implies(fd.getDeterminants(), fd.getDependents()); + }); + + return new FunctionalDependencySet(reducedFDs); + } + + /** + * Reduce left side by removing redundant columns from determinants. + */ + private static FunctionalDependency reduceLeft(FunctionalDependency fd, + FunctionalDependencySet fdSet) { + ImmutableBitSet determinants = fd.getDeterminants(); + ImmutableBitSet dependents = fd.getDependents(); + + // Try removing each attribute to find minimal determinant set + for (int attr : fd.getDeterminants()) { + ImmutableBitSet reduced = determinants.clear(attr); + if (fdSet.closure(reduced).contains(dependents)) { Review Comment: here I wonder whether the closure you computed previously could be reused to compute the new closure without starting from scratch ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { + if (!fd.isTrivial()) { + fdSet.add(fd); + } + } + + public void addFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(FunctionalDependency.of(determinants, dependents)); + } + + public void addBidirectionalFD(ImmutableBitSet determinants, ImmutableBitSet dependents) { + addFD(determinants, dependents); + addFD(dependents, determinants); + } + + public void addFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + } + + public void addBidirectionalFD(int determinant, int dependent) { + addFD(ImmutableBitSet.of(determinant), ImmutableBitSet.of(dependent)); + addFD(ImmutableBitSet.of(dependent), ImmutableBitSet.of(determinant)); + } + + public void removeFD(FunctionalDependency fd) { + fdSet.remove(fd); + } + + public Set<FunctionalDependency> getFDs() { + return Collections.unmodifiableSet(fdSet); + } + + /** + * Returns an ImmutableBitSet containing all attribute indexes that appear in any FD in the set. + */ + public static ImmutableBitSet allAttributesFromFDs(FunctionalDependencySet fds) { + ImmutableBitSet.Builder builder = ImmutableBitSet.builder(); + Set<FunctionalDependency> fdSet = fds.getFDs(); + for (FunctionalDependency fd : fdSet) { + builder.addAll(fd.getDeterminants()); + builder.addAll(fd.getDependents()); + } + return builder.build(); + } + + /** + * Computes the closure of a set of attributes under this functional dependency set. + * The closure of X, denoted X+, is the set of all attributes that can be functionally + * determined by X using the functional dependencies in this set and + * <a href="https://en.wikipedia.org/wiki/Armstrong%27s_axioms";>Armstrong's axioms</a> + * + * @param attributes the input attribute set + * @return the closure of the input attributes + */ + public ImmutableBitSet closure(ImmutableBitSet attributes) { + if (attributes.isEmpty()) { + return ImmutableBitSet.of(); + } + + // For large attribute sets, skip detailed closure computation to avoid performance issues + // The result may be an over-approximation + if (attributes.cardinality() > MAX_CLOSURE_ATTRS) { + return ImmutableBitSet.of(attributes); + } + + Set<Integer> closureSet = new HashSet<>(); + Queue<Integer> queue = new ArrayDeque<>(); + for (int attr : attributes) { + closureSet.add(attr); + queue.add(attr); + } + + Map<FunctionalDependency, Integer> fdMissingCount = new HashMap<>(); + Map<Integer, List<FunctionalDependency>> attrToFDs = new HashMap<>(); + for (FunctionalDependency fd : fdSet) { + fdMissingCount.put(fd, fd.getDeterminants().cardinality()); + for (int det : fd.getDeterminants()) { + attrToFDs.computeIfAbsent(det, k -> new ArrayList<>()).add(fd); + } + } + + while (!queue.isEmpty()) { + Integer attr = + requireNonNull(queue.poll(), "Queue returned null while computing closure"); + List<FunctionalDependency> fds = attrToFDs.get(attr); + if (fds == null) { + continue; + } + for (FunctionalDependency fd : fds) { + int missing = + requireNonNull(fdMissingCount.get(fd), "fdMissingCount returned null for FD " + fd); + missing = missing - 1; + fdMissingCount.put(fd, missing); + if (missing == 0) { + for (int dep : fd.getDependents()) { + if (closureSet.add(dep)) { + queue.add(dep); + } + } + } + } + } + + return ImmutableBitSet.of(closureSet); + } + + /** + * Check if X determined Y is implied by this FD set. + */ + public boolean implies(ImmutableBitSet determinants, ImmutableBitSet dependents) { + // Check if there is a direct FD match + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(determinants) + && fd.getDependents().contains(dependents)) { + return true; + } + } + return closure(determinants).contains(dependents); + } + + /** + * Check if a single column is functionally determined by another column. + */ + public boolean determines(int determinant, int dependent) { + // Check if there is a direct FD match + ImmutableBitSet detSet = ImmutableBitSet.of(determinant); + for (FunctionalDependency fd : fdSet) { + if (fd.getDeterminants().equals(detSet) + && fd.getDependents().get(dependent)) { + return true; + } + } + return closure(detSet).get(dependent); + } + + /** + * Compute the minimal cover of this functional dependency set. + * Returns an equivalent set with minimal dependencies. + */ + public FunctionalDependencySet minimalCover() { + // Split multi-attribute right sides into single attributes + Set<FunctionalDependency> splitFDs = new HashSet<>(); + for (FunctionalDependency fd : fdSet) { + splitFDs.addAll(fd.split()); + } + splitFDs.removeIf(FunctionalDependency::isTrivial); + + // Remove redundant attributes from left sides + Set<FunctionalDependency> reducedFDs = new HashSet<>(); + for (FunctionalDependency fd : splitFDs) { + if (fd.getDeterminants().cardinality() <= 1) { + reducedFDs.add(fd); + } else { + FunctionalDependencySet tempSet = new FunctionalDependencySet(splitFDs); + tempSet.removeFD(fd); + reducedFDs.add(reduceLeft(fd, tempSet)); + } + } + + // Remove redundant functional dependencies + reducedFDs.removeIf(fd -> { + FunctionalDependencySet remainingFDs = new FunctionalDependencySet(reducedFDs); + remainingFDs.removeFD(fd); + return remainingFDs.implies(fd.getDeterminants(), fd.getDependents()); + }); + + return new FunctionalDependencySet(reducedFDs); + } + + /** + * Reduce left side by removing redundant columns from determinants. + */ + private static FunctionalDependency reduceLeft(FunctionalDependency fd, + FunctionalDependencySet fdSet) { + ImmutableBitSet determinants = fd.getDeterminants(); + ImmutableBitSet dependents = fd.getDependents(); + + // Try removing each attribute to find minimal determinant set + for (int attr : fd.getDeterminants()) { + ImmutableBitSet reduced = determinants.clear(attr); + if (fdSet.closure(reduced).contains(dependents)) { + determinants = reduced; + } + } + return FunctionalDependency.of(determinants, dependents); + } + + /** + * Check if this FD set is equivalent to another FD set. + * Two FD sets are equivalent if they have the same closure for any attribute set. + */ + public boolean equalTo(FunctionalDependencySet other) { + for (FunctionalDependency fd : fdSet) { + if (!other.implies(fd.getDeterminants(), fd.getDependents())) { + return false; + } + } + + for (FunctionalDependency fd : other.fdSet) { + if (!implies(fd.getDeterminants(), fd.getDependents())) { + return false; + } + } + + return true; + } + + /** + * Find candidate keys within the given attribute set. + * + * @param attributes the set of attributes to search for candidate keys within + * @param onlyMinimalKeys if true, only return minimal candidate keys (shortest length); + * if false, return all minimal candidate keys + * @return a set of attribute subsets that can determine all given attributes + */ + public Set<ImmutableBitSet> findCandidateKeys( + ImmutableBitSet attributes, boolean onlyMinimalKeys) { + // Branch and bound algorithm for minimal candidate key search + if (fdSet.isEmpty()) { + return ImmutableSet.of(attributes); + } + + // Attributes that are not dependents of any FD + ImmutableBitSet essentialAttrs = findEssentialAttributes(attributes); + if (closure(essentialAttrs).contains(attributes)) { + return ImmutableSet.of(essentialAttrs); + } + + Set<ImmutableBitSet> result = new HashSet<>(); + int minKeySize = Integer.MAX_VALUE; + PriorityQueue<ImmutableBitSet> queue = + new PriorityQueue<>(Comparator.comparingInt(ImmutableBitSet::cardinality)); + Set<ImmutableBitSet> visited = new HashSet<>(); + queue.add(essentialAttrs); + + while (!queue.isEmpty()) { + ImmutableBitSet cand = + requireNonNull(queue.poll(), "Queue returned null while searching candidate keys"); + if (visited.contains(cand)) { + continue; + } + visited.add(cand); + if (onlyMinimalKeys && cand.cardinality() > minKeySize) { + break; + } + + // If a candidate key is a superset of key, It is a redundant set + boolean covered = false; + for (ImmutableBitSet key : result) { + if (cand.contains(key)) { + covered = true; + break; + } + } + + if (covered) { + continue; + } + + ImmutableBitSet candClosure = closure(cand); + if (candClosure.contains(attributes)) { + result.add(cand); + if (onlyMinimalKeys) { + minKeySize = cand.cardinality(); + } + continue; + } + + // Expand: only add attributes not in the closure + ImmutableBitSet remain = attributes.except(cand); + for (int attr : remain) { + if (candClosure.get(attr)) { + continue; + } + ImmutableBitSet next = cand.set(attr); + if (!visited.contains(next)) { + queue.add(next); + } + } + } + return result.isEmpty() ? ImmutableSet.of(attributes) : result; + } + + private ImmutableBitSet findEssentialAttributes(ImmutableBitSet attributes) { + // Find attributes that do not appear on the right side of any FD (essential for key) Review Comment: I do not understand the comment about "essential for key" ########## core/src/main/java/org/apache/calcite/rel/metadata/FunctionalDependencySet.java: ########## @@ -0,0 +1,420 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to you under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +package org.apache.calcite.rel.metadata; + +import org.apache.calcite.util.ImmutableBitSet; + +import com.google.common.collect.ImmutableSet; + +import java.util.ArrayDeque; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.HashMap; +import java.util.HashSet; +import java.util.List; +import java.util.Map; +import java.util.PriorityQueue; +import java.util.Queue; +import java.util.Set; + +import static java.util.Objects.requireNonNull; + +/** + * A set of functional dependencies with closure and minimal cover operations. + * This class implements standard algorithms for functional dependency reasoning. + */ +public class FunctionalDependencySet { + // Maximum number of transitive closure iterations to prevent infinite loops + public static final int MAX_TRANSITIVE_CLOSURE_LOOPS = 10; + // Maximum number of attributes supported in closure computation + private static final int MAX_CLOSURE_ATTRS = 10000; + + private final Set<FunctionalDependency> fdSet = new HashSet<>(); + + public FunctionalDependencySet() {} + + public FunctionalDependencySet(Set<FunctionalDependency> fds) { + this.fdSet.addAll(fds); + } + + public void addFD(FunctionalDependency fd) { Review Comment: can somehow the functions that mutate `this` be documented? Some operations, like `union` are functional, others, like `add` are not. (it's true that add returns void, but this doesn't preclude having a variant of `add` that returns `this`.) ########## core/src/main/java/org/apache/calcite/rel/metadata/RelMdFunctionalDependency.java: ########## @@ -20,33 +20,47 @@ import org.apache.calcite.plan.RelOptUtil; import org.apache.calcite.rel.RelNode; import org.apache.calcite.rel.core.Aggregate; -import org.apache.calcite.rel.core.AggregateCall; import org.apache.calcite.rel.core.Calc; import org.apache.calcite.rel.core.Correlate; +import org.apache.calcite.rel.core.Filter; import org.apache.calcite.rel.core.Join; +import org.apache.calcite.rel.core.JoinRelType; import org.apache.calcite.rel.core.Project; import org.apache.calcite.rel.core.SetOp; import org.apache.calcite.rel.core.TableScan; import org.apache.calcite.rex.RexCall; import org.apache.calcite.rex.RexInputRef; +import org.apache.calcite.rex.RexLiteral; import org.apache.calcite.rex.RexNode; -import org.apache.calcite.rex.RexProgram; import org.apache.calcite.rex.RexUtil; +import org.apache.calcite.sql.SqlKind; import org.apache.calcite.util.ImmutableBitSet; +import org.apache.calcite.util.mapping.Mappings; import org.checkerframework.checker.nullness.qual.Nullable; +import java.util.HashMap; import java.util.List; +import java.util.Map; +import java.util.Set; /** - * Default implementation of - * {@link RelMetadataQuery#determines(RelNode, int, int)} + * Default implementation of {@link BuiltInMetadata.FunctionalDependency} metadata handler Review Comment: This class could have been left for a separate PR; this one is very large. -- This is an automated message from the Apache Git Service. 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