Improving the Performance of Graph Coloring Algorithms through Backtracking

  • Authors:

  • Sanjukta Bhowmick;Paul D. Hovland

  • Affiliations:

  • Department of Computer Science and Engineering, The Pennsylvania State University, University Park PA 16802;Mathematics and Computer Science Division, Argonne National Laboratory, Argonne IL 60439-4844

  • Venue:
  • ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
  • Year:
  • 2008

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Abstract

Graph coloring is used to identify independent objects in a set and has applications in a wide variety of scientific and engineering problems. Optimal coloring of graphs is an NP-complete problem. Therefore there exist many heuristics that attempt to obtain a near-optimal number of colors. In this paper we introduce a backtracking correction algorithm which dynamically rearranges the colors assigned by a top level heuristic to a more favorable permutation thereby improving the performance of the coloring algorithm. Our results obtained by applying the backtracking heuristic on graphs from molecular dynamics and DNA-electrophoresis show that the backtracking algorithm succeeds in lowering the number of colors by as much as 23%. Variations of backtracking algorithm can be as much as 66% faster than standard correction algorithms, like Culberson's Iterated Greedy method, while producing a comparable number of colors.