Two files are included, both taken from a project working with approximation
algorithms for planar graphs as part of my most recent research work.



The first file "interface.h" defines a particular family of dynamic programs which
was often the final step -- and computational bottleneck -- for the graph algorithms
that were being implemented in this project. I want to draw particular attention to
the methods "run_parallel" and "handle_merge" which do much of the work.

The method "run_parallel" uses Intel's Thread Building Block library to allow
independent sub-problems in the dynamic program to execute in parrallel.
In particular it uses a flow graph to describe data dependency between sub-problems,
allowing the main storage to be nothing more than a std:vector.

The method "handle_merge" handles the general case of the dynamic program: using two
previous results as dependencies, it matches partial solutions for compatibility,
composes them, and stores the result for later use.



The second file "mehlhorn_steiner_twoappox.h" implements a simpler algorithm, first
described in the paper "A Faster Approximation Algorithm for the Steiner Problem in Graphs"
(Mehlhorn 1988). The algorithm takes a graph and a set of vertices then returns edges that
form a tree touching each vertex in the input set.

A few technical notes:
 * Think of "Dart" as "directed edge"
 * "Table", "NodeSet" and "DartSet" allow constant time lookup and insertion.
 * "SPTree" is "Shortest Path Tree" computed with a priority queue.
 * "MST" is "Minimal Spanning Tree" computed with Prim's algorithm.