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Computing

, Volume 36, Issue 1–2, pp 1–16 | Cite as

On a circle placement problem

  • B. M. Chazelle
  • D. T. Lee
Contributed Papers

Abstract

We consider the following circle placement problem: given a set of pointsp i ,i=1,2, ...,n, each of weightw i , in the plane, and a fixed disk of radiusr, 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 setS ofn circles,D i ,i=1,2, ...,n, of the same radiusr, each of weightw i , find a subset ofS whose common intersection is nonempty and whose total weight is maximum. AnO (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 inO (n2 logn) time.

Keywords

Sorting Computational Mathematic Total Weight Maximum Clique Intersection Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Über ein Problem der Kreisscheibenplazierung

Zusammenfassung

Diese Arbeit untersucht das folgende Optimierungsproblem: gegeben sei eine Menge von PunktenP i ,i=1,2, ...,n, in der Ebene, jeder mit Gewichtw i , und eine Kreisscheibe mit vorgegebenem Radius; finde eine Plazierung der Kreisscheibe, die die Summe der Gewichte aller überdeckten Punkte maximiert. Dieses Problem ist äquivalent zum folgenden Problem definiert für den Schnittgraphen vonn kongruenten gewichteten Kreisscheiben in der Ebene: bestimme eine Clique (die korrespondierenden Kreisscheiben haben einen nichtleeren gemeinsamen Durchschnitt), die die Summe der Gewichte maximiert. Wir präsentieren einenO (n2)-Algorithmus für dieses Problem, was eine Verbesserung darstellt gegenüber dem besten bisher bekannten Algorithmus, der sortiert undO (n2 logn) an Laufzeit benötigt.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • B. M. Chazelle
    • 1
  • D. T. Lee
    • 2
  1. 1.Department of Computer ScienceBrown UniversityProvidenceU.S.A.
  2. 2.Department of Electrical Engineering/Computer ScienceNorthwestern UniversityEvanstonU.S.A.

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