Extremal Optimization of Graph Partitioning at the Percolation Threshold

TL;DR

This paper demonstrates that Extremal Optimization outperforms Simulated Annealing in graph partitioning near the percolation threshold, especially for large, sparse graphs, by leveraging self-organized criticality dynamics.

Contribution

It introduces and evaluates Extremal Optimization as a superior method for graph partitioning at the percolation threshold, outperforming traditional approaches.

Findings

Extremal Optimization reduces relative error compared to Simulated Annealing near the critical point.

Performance advantage is more pronounced for large, sparse graphs.

Extremal Optimization reproduces known critical partition results effectively.

Abstract

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.