Set Cover Problems with Small Neighborhood Covers

In this paper, we study a class of set cover problems that satisfy a special property which we call the small neighborhood cover property. This class encompasses several well-studied problems including vertex cover, interval cover, bag interval cover and tree cover. We design unified sequential, parallel and distributed algorithms that can handle any set cover problem falling under the above framework and yield constant factor approximations. The algorithms run in NC in the parallel setting and can be executed in polylogarithmic communication rounds in the distributed setting.