xiedeyantu commented on code in PR #4540: URL: https://github.com/apache/calcite/pull/4540#discussion_r2384382587
########## 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: For example, if I input an attributes set {0, 1, 2, 5}, and the fdSet is [{0} → {1, 2}], then during the initial phase, the candidate key would find a minimal required set {0, 5}. This is because if the dependents are {1, 2}, there must be a determinants set {0} that determines them. Therefore, {1, 2} definitely cannot be a candidate key. -- This is an automated message from the Apache Git Service. To respond to the message, please log on to GitHub and use the URL above to go to the specific comment. To unsubscribe, e-mail: [email protected] For queries about this service, please contact Infrastructure at: [email protected]
