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

TL;DR

This paper investigates the energy landscapes of two spin glass models using a greedy single-spin flipping process, demonstrating its effectiveness in approaching ground states for the random maximum 2-satisfiability problem but limitations in the Viana-Bray model.

Contribution

It introduces and analyzes the Gmax greedy process for exploring energy landscapes, highlighting its success in the maximum 2-satisfiability problem and its limitations in other models.

Findings

Gmax efficiently approaches the ground-state energy density in the maximum 2-satisfiability problem.

The energy density decreases logarithmically with time, indicating a rugged funnel-shaped landscape.

Gmax quickly gets trapped in local minima in the Viana-Bray spin glass model.

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.