摘要：We study a clustering problem where the goal is to maximize the coverage of the input points by k chosen centers. Specifically, given a set of n points P âS â"^d, the goal is to pick k centers C âS â"^d that maximize the service â^'_{pâ^^P}Ï(ð-½(p,C)) to the points P, where ð-½(p,C) is the distance of p to its nearest center in C, and Ï is a non-increasing service function Ï: â"+ â' â"+. This includes problems of placing k base stations as to maximize the total bandwidth to the clients - indeed, the closer the client is to its nearest base station, the more data it can send/receive, and the target is to place k base stations so that the total bandwidth is maximized. We provide an n^{ε^-O(d)} time algorithm for this problem that achieves a (1-ε)-approximation. Notably, the runtime does not depend on the parameter k and it works for an arbitrary non-increasing service function Ï: â"+ â' â"+.
