Improved Exact and Heuristic Algorithms for Maximum Weight Clique

TL;DR

This paper introduces improved exact and heuristic algorithms for the maximum weight clique problem, utilizing novel data reduction rules and demonstrating superior performance on various graph datasets.

Contribution

The paper presents novel data reduction techniques integrated into algorithms that significantly enhance solution speed and quality for the maximum weight clique problem.

Findings

Exact algorithm MWCRedu is much faster on medium-sized graphs.

Heuristic algorithm MWCPeel outperforms competitors on key benchmarks.

Data reductions produce smaller graphs than previous methods.

Abstract

We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data reduction rules that use local graph structure to identify and remove vertices and edges while retaining the optimal solution. We evaluate our algorithms on a range of synthetic and real-world graphs, and find that they outperform the current state of the art on most inputs. Our data reductions always produce smaller reduced graphs than existing data reductions alone. As a result, our exact algorithm, MWCRedu, finds solutions orders of magnitude faster on naturally weighted, medium-sized map labeling graphs and random hyperbolic graphs. Our heuristic algorithm, MWCPeel, outperforms its competitors on these instances, but is slightly less effective on extremely dense or large instances.