A Maximum Profit Coverage Algorithm with Application to Small Molecules Cluster Identification

On approximating four covering and packing problems

“…Our inapproximability constant for the triangle packing problem improves upon the previous results in [16,19]; this is done by directly transforming the inapproximability gap of Håstad for the problem of maximizing the number of satisfied equations for a set of equations over GF (2) [26] and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al [6,7] and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or [25].…”

“…MPC has applications in clustering identification of molecules [25]. The 2-coverage problem has motivations in optimizing multiple spaced seeds for homology search (for relevant concepts, see e.g.…”

“…Maximum Profit Coverage Problem (MPC) [25] We have family of m sets S over a universe U of n elements. For each A ∈ S we have a non-negative cost q A and for each i ∈ U we have a nonnegative profit w i .…”