A family of greedy algorithms for finding maximum independent sets

TL;DR

This paper introduces a family of greedy algorithms designed to find maximum independent sets in graphs, utilizing heuristics and initial set sizes to iteratively build larger independent sets.

Contribution

It proposes a flexible greedy framework that can incorporate different heuristics and initial conditions for finding large independent sets in graphs.

Findings

Effective in finding large independent sets

Flexible with various heuristics and initial parameters

Applicable to different graph types

Abstract

The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for any of the sets. The algorithms receives as arguments the graph, the heuristic used to evaluate the independent set candidates, and the initial cardinality of the independent sets, and returns the final set of independent sets.