A parallel distance-2 graph coloring algorithm for distributed memory computers

Authors:
Doruk Bozdağ;Umit Catalyurek;Assefaw H. Gebremedhin;Fredrik Manne;Erik G. Boman;Füsun Özgüner
Affiliations:
Ohio State University;Ohio State University;Old Dominion University;University of Bergen, Norway;Sandia National Laboratories;Ohio State University
Venue:
HPCC'05 Proceedings of the First international conference on High Performance Computing and Communications
Year:
2005

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Abstract

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than two from each other. Application examples include numerical optimization and channel assignment. We present the first distributed-memory heuristic algorithm for this NP-hard problem. Parallel speedup is achieved through graph partitioning, speculative (iterative) coloring, and a BSP-like organization of computation. Experimental results show that the algorithm is scalable, and compares favorably with an alternative approach—solving the problem on a graph G by first constructing the square graph G2 and then applying a parallel distance-1 coloring algorithm on G2.