Team Vertex Jimmy Fifield Nick Marino

Graph Coloring What is the minimum number of colors needed to color every vertex so that no neighboring vertexes are the same color? NP-Complete problem. Brute force is extremely inefficient as number of colorings increases factorially.

Deletion-Contraction Algorithm Recursive. X(G) = min{ X(G + uv), X(G / uv) } u and v cannot be adjacent vertices.

Sequential Program Graph.java GraphInputReader.java ColoringCore.java ColoringCoreSeq.java ColoringCoreMain.java ColoringSeq.java

Graph Represents a simple graph composed of vertices and edges. Abstracts away the data structure implementation details, Provides a way to perform simple operations on the graph (adding/deleting an edge, contracting two vertices,etc).

GraphInputReader This class takes an input file name in the constructor, and then provides a method to read the file, parse the contents, and create a new Graph object based on the results.

ColoringCore Interface Provides the specifications for a graph coloring solver. There's a single method - run - that takes a Graph as input and returns the chromatic number of that graph.

ColoringCoreSeq Provides a sequential implementation of the deletion-contraction algorithm.

ColoringMain This class takes the command line arguments and a ColoringCoreobject. Input. Timing measurements. Utilizes the ColoringCore to calculate the answer.

ColoringSeq Creates a new sequential core. Starts the main program.

Parallel Program Graph.java GraphInputReader.java ColoringCore.java ColoringCoreSMP.java ColoringCoreMain.java ColoringSMP.java

ColoringCoreSMP

ColoringSMP

Performance Metrics

What We Learned

Future Work