Generic weight types and updated shortest path implementations
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                 Key: SANDBOX-356
                 URL: https://issues.apache.org/jira/browse/SANDBOX-356
             Project: Commons Sandbox
          Issue Type: Improvement
          Components: Graph
            Reporter: Claudio Squarcella
         Attachments: 
GenericWeightTypesAndUpdatedShortestPathImplementations.patch

Hello,

with this issue I propose quite a major improvement to the current version of 
Apache Commons Graph, aimed at introducing generic types for weights (edge 
weights, vertex weights, etc) and decoupling related properties and operations 
using external classes. The proposed changes reflect observations and proposals 
that have been evaluated on the dev mailing list, particularly in the thread 
with title "On graph weight type(s)".

A new top level package {{weight}} contains a hierarchy of interfaces 
representing different "families" of weights with their properties and 
operations: {{Zero}}, {{Semigroup}}, {{Monoid}}, {{OrderedMonoid}}. These 
interfaces are meant to be specified as input by different algorithms depending 
on the properties needed: e.g. some only require an ordering on the weights, 
some apply operations, etc. A subpackage called {{primitive}} contains two 
implementations, {{DoubleWeight}} and {{IntegerWeight}}, respectively wrapping 
properties and operations on weights of type {{Double}} and {{Integer}}.

In addition, some of the implementations in the package {{shortestpath}} have 
been updated to take advantage of the new generic weight types. In particular 
each of the three classes {{Dijkstra}}, {{BellmannFord}} and {{FloydWarshall}} 
now has two public methods: a generic one (working with any kind of weight, 
provided an {{OrderedMonoid}}) and a "shortcut" for weights of type {{Double}}, 
which is basically identical to the current signature. Other classes in the 
package were subject to minor changes to support the improvements. As an 
exception, {{AStar}} is still tied to {{Double}} weights for now: as a future 
step that could also use generic weights (but it needs more thinking for the 
heuristics).

Further, in order to handle generic weight types, I got rid of 
{{Double.POSITIVE_INFINITY}} as a way to represent unreachability between two 
endpoints in a graph and replaced it with related boolean methods.

Finally, all the tests were updated for compatibility with the new signatures, 
and they all run smoothly.

I hope this patch meets the approval of other developers/users. I am available 
for discussion and clarification.

Ciao,
Claudio

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