### Abstract

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.

Original language | English (US) |
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Pages | 333-337 |

Number of pages | 5 |

State | Published - Dec 1 1984 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*ON A CIRCLE PLACEMENT PROBLEM.*. 333-337.