FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

Abstract

Finding large (and generally maximal) independent sets of vertices in a given graph is a fundamental problem in distributed computing. Applications include, for example, facility location and backbone formation in wireless ad hoc networks. In this paper we study a decentralized (or distributed) algorithm inspired by the calling behaviour of male Japanese tree frogs, originally introduced for the graph coloring problem, for its potential usefulness in the context of finding large independent sets. Moreover, we adapt this algorithm to directly produce maximal independent sets without the necessity of first producing a graph coloring solution. Both algorithms are compared to a wide range of decentralized algorithms from the literature on a diverse set of benchmark instances for the maximal independent set problem. The results show that both algorithms compare very favorably to their competitors.

scmamp: Statistical Comparison of Multiple Algorithms in Multiple Problems

“…Thus the results matrix we will use contains in each row the result obtained by each algorithms for a given problem. This dataset is part of the results in Blum et al (2015), and it is also included in the package. The first two columns indicate the size and the density of the random graph while the last eight columns contain the results obtained by each algorithm.…”

“…Thus, a post-hoc test (Friedman + Finner's correction) can be conducted to detect differences by pairs. > res <-postHocTest(data = dataset.means, algorithms = 3:10, test = friedman + correct = finner , control = FrogCOL ) Finally, for the third example we will use the same dataset from Blum et al (2015). In this example we want to compare the algorithms separately for every value of Radius given a fixed Size.…”

“…Under some circumstances we may be interested in analyzing the results in different groups of problems. An example of such a situation are the results presented in Blum et al (2015), where the behavior of a set of algorithms was tested in problems of different size and complexity 1 . In order to deal with these kinds of problems, conversely to other existing tools, the package offers the possibility of subsetting the results, which can be handy when the problems can be subdivided into different groups (e.g., based on their size).…”