ON A CIRCLE PLACEMENT PROBLEM.

We consider the following circle placement problem: given a set of points p//i, i equals 1, 2, . . . ,n, each of weight w//i, in the plane, and a fixed disk of radius r, find a location to place the disk such that the total weight of the points covered by the disk is maximized. The problem is equivalent to the so-called maximum weighted clique problem for circle intersection graphs. That is, given a set S of n circles, D//i, i equals 1, 2, . . . , n, of the same radius r, each of weight w//i, find a subset of S whose common intersection is nonempty and whose total weight is maximum. An O(n**2) algorithm is presented for the maximum clique problem. The algorithm is better than a previously known algorithm which is based on sorting and runs in O(n**2logn) time.