We consider the following circle placement problem: given a set of points pi, i=1,2, ..., n, each of weight wi, 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, Di, i=1,2, ..., n, of the same radius r, each of weight wi, find a subset of S whose common intersection is nonempty and whose total weight is maximum. An O (n2) 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 (n2 log n) time.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics