Vertex cover problem studied by cavity method: Analytics and population dynamics
Abstract
We study the vertex cover problem on finite connectivity random graphs by zero-temperature cavity method. The minimum vertex cover corresponds to the ground state(s) of a proposed Ising spin model. When the connectivity c>e=2.718282, there is no state for this system as the reweighting parameter y, which takes a similar role as the inverse temperature \beta in conventional statistical physics, approaches infinity; consequently the ground state energy is obtained at a finite value of y when the free energy function attains its maximum value. The minimum vertex cover size at given c is estimated using population dynamics and compared with known rigorous bounds and numerical results. The backbone size is also calculated.
Keywords
Cite
@article{arxiv.cond-mat/0302289,
title = {Vertex cover problem studied by cavity method: Analytics and population dynamics},
author = {Haijun Zhou},
journal= {arXiv preprint arXiv:cond-mat/0302289},
year = {2009}
}
Comments
7 pages (including 3 figures and 1 table), REVTeX4 format