Experiments With Parallel Graph Coloring Heuristics and Applications of Graph Coloring (1993) [18 citations — 0 self]
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@INPROCEEDINGS{Lewandowski93experimentswith,author = {Gary Lewandowski and Anne Condon},
title = {Experiments With Parallel Graph Coloring Heuristics and Applications of Graph Coloring},
booktitle = {In (Johnson & Trick},
year = {1993},
pages = {309--334},
publisher = {American Mathematical Society}
}
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Abstract:
Abstract. We introduce a new hybrid graph coloring algorithm, which combines a parallel version of Morgenstern's S-Impasse algorithm [26], with exhaustive search. Our goal is progress towards a coloring heuristic that works well without extensive tuning of algorithm parameters. We also contribute new test data arising in five different application domains, including register allocation and course scheduling. Hybrid was implemented on a Connection Machine CM-5, and tested on the application data as well as several types of randomly generated graphs. The results are compared with results of two simple sequential heuristics, the Saturation algorithm of Br'elaz [5] and the Recursive Largest First (RLF) algorithm of Leighton [24], as well as with previous work reported by Morgenstern [26] and Johnson et al. [17]. On many random graphs, the performance of Hybrid without tuning of parameters is comparable or better than tuned sequential algorithms; on large random graphs, Hybrid does not come close to the best colorings found by tuned time-intensive algorithms such as XRLF [17] and Morgenstern's tuned S-Impasse [26]. Of the application data, three applications are easily colored even by the simple sequential heuristics; one (the course scheduling data) is optimally colored by Hybrid but not by the simple heuristics, and one appears to be very hard. In several cases, however, we found that finding an optimal coloring is not sufficient to solve the problem at hand, rather colorings satisfying additional restrictions are needed. We find that the course scheduling applications is not well-modeled by random graphs, which suggests that more application data should be collected for testing heuristics and that new random generators are needed to model these problems.
