We improve the status quo in two ways: for the unweighted case, we show how to obtain a PTAS using the framework recently proposed (independently) by Mustafa and Ray [16] and by Chan and Har-Peled [4].Expand

We consider the problem of computing a minimum cost <i>k</i>-cover for a given set of balls, denoted cost(<i>P</i>, whose union covers (contains) a set of at most k balls.Expand

We show that a k-fold covering using translates of an arbitrary convex polygon can be decomposed into Omega(k) covers (using an efficient algorithm).Expand

We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations and show the existence of a planar graph that appropriately relates the global optimum.Expand

We improve the status quo in two ways: for the unweighted case, we show how toobtain a PTAS using the framework recently proposed (independently) by Mustafa and Ray [16] and byChan and Har-Peled [4]; for the weighted case where each input disk has an associated rational weightwith the objective of ﬁnding a minimum cost dominating set.Expand