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arXiv · 1104.2656

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

Hui Ma·Haijun Zhou
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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.

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Hui Ma, Haijun Zhou. 2011-04-14. Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process. https://doi.org/10.1103/physreve.83.052101

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