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Facility dispersion problems: Heuristics and special cases

  • S. S. Ravi
  • D. J. Rosenkrantz
  • G. K. Tayi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4(\(\sqrt 2 - 1\)) ≈ 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.

Keywords

Polynomial Time Triangle Inequality Edge Weight Polynomial Time Algorithm Optimal Placement 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • S. S. Ravi
    • 1
  • D. J. Rosenkrantz
    • 1
  • G. K. Tayi
    • 2
  1. 1.Department of Computer ScienceSUNY at AlbanyAlbany
  2. 2.School of Business AdministrationSUNY at AlbanyAlbany

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