2001/04/12 by Stefan Boettcher, S. Boettcher, Allon G. Percus +1 · 5 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Combinatorics #Complexity and Algorithms in Graphs #Computer science #Convergence (economics) #Extremal optimization #Function (biology) #Graph #Low-power high-performance VLSI design #Mathematical optimization #Mathematics #Meta-optimization #Optimization problem #Random graph #Scaling #Simple (philosophy) #VLSI and FPGA Design Techniques #cond-mat.stat-mech #cs.NE #math.OC
paper · pdf · doi:10.1103/physreve.64.026114
published as Phys. Rev. E, 64 (2001) 026114 · 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher/
arxiv created 2001/04/12 · openalex publication_date 2001/07/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the computationally hard (NP-hard) graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of run time and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. On random graphs, our numerical results demonstrate that extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over run time roughly as a power law t(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.