An exhaustive search algorithm can solve the problem in time 2"k""n""O"(1), where "k" is the size of the vertex cover. Vertex cover is therefore fixed-parameter tractable, and if we are only interested in small "k", we can solve the problem in polynomial time. One algorithmic technique that works here is called "bounded search tree algorithm", and its idea is to repeatedly choose some vertex and recursively branch, with two cases at each step: place either the current vertex or all its neighbours into the vertex cover.