Semidefinite Relaxation for the Dominating Set Problem

It is a well-known fact that finding a minimum dominating set and consequently finding the domination number of a general graph is an NP-complete problem. Here, we first model this problem as nonlinear binary optimization problems and then extract two closely related semidefinite relaxations. For each of these relaxations, different rounding algorithms are exploited to produce near-optimal dominating sets. Feasibility of the generated solutions and efficiency of the algorithms are analyzed.