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Vertex cover problem studied by cavity method: Analytics and population dynamics

Haijun Zhou
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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 βin 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.

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BibTeXRIS

Haijun Zhou. 2003-02-14. Vertex cover problem studied by cavity method: Analytics and population dynamics. https://doi.org/10.1140/epjb%2Fe2003-00096-4

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