A factor 2 approximation algorithm for the vertex cover P3P3 problem

We consider the vertex cover  PnPn (VCPnVCPn) problem, that is, the problem of finding a minimum weight set F⊂VF⊂V such that the graph G[V−F]G[V−F] has no PnPn, where PnPn is a path with n   vertices. The problem also has its application background. In this paper, we restrict our attention to the VCP3VCP3 problem and give a 2-approximation algorithm using the technique of layering.

► In the article we translate the camera layout problem into the vertex cover PnPn problem in graph theory.
► We first proved two important inequalities on the problem to show the main result.
► We designed an approximation algorithm to solve the vertex cover P3P3 problem.
► We proved the performance factor of the algorithm is no more than 2.