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Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process

By Hui Ma and Haijun Zhou

Abstract

In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, {\tt Gmax}. The ground-state energy density of the random maximum two-satisfiability problem is efficiently approached by {\tt Gmax}. The achieved energy density $e(t)$ decreases with the evolution time $t$ as $e(t)-e(\infty)=h (\log_{10} t)^{-z}$ with a small prefactor $h$ and a scaling coefficient $z > 1$, indicating an energy landscape with deep and rugged funnel-shape regions. For the $\pm J$ Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.Comment: 5 pages with 4 figures included. Accepted for publication in Physical Review E as a brief repor

Topics: Condensed Matter - Disordered Systems and Neural Networks
Year: 2011
DOI identifier: 10.1103/PhysRevE.83.052101
OAI identifier: oai:arXiv.org:1104.2656
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