Clustering analysis of the ground-state structure of the vertex-cover problem

Details Clustering analysis of the ground-state structure of the vertex-cover problem Clustering analysis of the ground-state structure of the vertex-cover problem

2004-03-07

arxiv.org/abs/cond-mat/0403193v2

Phys. Rev. E 70, 066120 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 10 figures

Scientific paper

10.1103/PhysRevE.70.066120

Vertex cover is one of the classical NP-complete problems in theoretical computer science. A vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset. When studied on Erdos-Renyi random graphs (with connectivity c) one observes a threshold behavior: In the thermodynamic limit the size of the minimal vertex cover is independent of the specific graph. Recent analytical studies show that on the phase boundary, for small connectivities c

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