Heuristics for Maximum Clique and Independent Set

Heuristics For Maximum Clique And Independent Set

Clique, independent set, and graph coloring

This article introduces the closely related maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems. The survey includes some of the most important results concerning these problems, including their computational complexity, known bounds, mathematical programming formulations, and exact and heuristic algorithms to solve them.

A new exact algorithm for the maximum-weight clique problem based on a heuristic vertex-coloring and a backtrack search

In this paper we present an exact algorithm for the maximum-weight clique problem on arbitrary undirected graphs. The algorithm based on a fact that vertices from the same independent set couldn’t be included into the same maximum clique. Those independent sets are obtained from a heuristic vertex coloring where each of them is a color class. Color classes and a backtrack search are used for pr...

Some Experimental and Theoretical Results on Test Case Generators for the Maximum Clique Problem

We describe and analyze test case generators for the maximum clique problem (or equivalently for the maximum independent set or vertex cover problems). The generators produce graphs with speci ed number of vertices and edges, and known maximum clique size. The experimental hardness of the test cases is evaluated in relation to several heuristics for the maximum clique problem, based on neural n...

On Maximum Weight Clique Algorithms, and How They Are Evaluated

Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algor...