Greedy, prohibition, and reactive heuristics for graph partitioning

New heuristic algorithms are proposed for the Graph Partitioning problem. A greedy construction scheme with an appropriate tie-breaking rule (MIN-MAX-GREEDY) produces initial assignments in a very fast time. For some classes of graphs, independent repetitions of MIN-MAX-GREEDY are sufficient to reproduce solutions found by more complex techniques. When the method is not competitive, the initial assignments are used as starting points for a prohibition-based scheme, where the prohibition is chosen in a randomized and reactive way, with a bias towards more successful choices in the previous part of the run. The relationship between prohibition-based diversification (Tabu Search) and the variable-depth Kernighan-Lin algorithm is discussed. Detailed experimental results are presented on benchmark suites used in the previous literature, consisting of graphs derived from parametric models (random graphs, geometric graphs, etc.) and of "real-world" graphs of large size. On the first series of graphs, a better performance for equivalent or smaller computing times is obtained, while, on the large "real-world" instances, significantly better results than those of multilevel algorithms are obtained, but for a much larger computational effort.