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.
Extended abstract
Research supported by NSF Grants CCR-88-03278, CCR-89-05296 and CCR-90-06396.
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© 1991 Springer-Verlag Berlin Heidelberg
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Ravi, S.S., Rosenkrantz, D.J., Tayi, G.K. (1991). Facility dispersion problems: Heuristics and special cases. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028275
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DOI: https://doi.org/10.1007/BFb0028275
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