An Empirical Study of Two MIS Algorithms

Distributed algorithms for computing a maximal independent set of a graph have been very popular in the research community. Starting with the algorithm of Luby dating back to 25 years, several researchers have focused on distributed MIS algorithms for general graphs. with little success. Only recently, M´etevier et al. have proposed an algorithm for MIS in the distributed setting with a round complexity that matches Luby´s algorithm asymptotically. However, very little is known about the relative performance of the algorithm of Luby and M´etevier in practice. Such a study can throw light on some aspects of the algorithms that are not brought out by a theoretical analysis. In this paper, we compare implementations of the algorithm of Luby and M´etevier and study their behavior on a class of random graphs and bipartite graphs. Further, we study how varying the probability that a node wishes to join the MIS in the case of Luby´s algorithm affects the number of rounds required.