Message passing for vertex covers

Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message-passing techniques, namely, warning and survey propagation, which serve as efficient heuristic algorithms for solving these computational hard problems. We show also, how previously obtained results on the typical-case behavior of vertex covers of random graphs can be recovered starting from the message-passing equations, and how they can be extended.