article

Heuristic and Special Case Algorithms for Dispersion Problems

Operations Research, Volume 42, Issue 2

Pages 299 - 310

https://doi.org/10.1287/opre.42.2.299

Published: 01 April 1994 Publication History

Abstract

<P>The dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities. The problem also arises in selecting nondominated solutions for multiobjective decision making. It is known to be NP-hard under two objectives: maximizing the minimum distance MAX-MIN between any pair of facilities and maximizing the average distance MAX-AVG. We consider the question of obtaining near-optimal solutions. for MAX-MIN, 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 satisfy the triangle inequality, we analyze an efficient heuristic and show that it provides a performance guarantee of two. We also prove that obtaining a performance guarantee of less than two is NP-hard. for MAX-AVG, we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality. We also present a polynomial-time algorithm for the 1-dimensional MAX-AVG dispersion problem. Using that algorithm, we obtain a heuristic which provides an asymptotic performance guarantee of π/2 for the 2-dimensional MAX-AVG dispersion problem.</P>

References

[1]

CHURCH, R. L., AND R. S. GARFINKEL. 1978. Locating an Obnoxious Facility on a Network. Trans. Sci. 12, 107-118.

Digital Library

[2]

CHANDRASEKHARAN, R., AND A. DAUGHETY. 1981. Location on Tree Networks: p-Centre and n-Dispersion Problems. Math. Opns. Res. 6, 50-57.

Digital Library

[3]

DASARATHY, B., AND L. J. WHITE. 1980. A Maxmin Location Problem. Opns. Res. 28, 1385-1401.

Digital Library

[4]

ERKUT, E. 1990. The Discrete p-Dispersion Problem. Eur. J. Opnl. Res. 46, 48-60.

[5]

ERKUT, E., AND S. NEUMAN. 1989. Analytical Models for Locating Undesirable Facilities. Eur. J. Opnl. Res. 40, 275-291.

[6]

ERKUT, E., AND S. NEUMAN. 1990. Comparison of Four Models for Dispersing Facilities. INFOR 29, 68-85.

[7]

ERKUT, E., AND T. S. ÖNCÜ. 1991. A Parametric 1- Maximin Location Problem. J. Opnl. Res., Soc. 42, 49-55.

[8]

ERKUT, E., T. BAPTIE AND B. VON HOHENBALKEN. 1990. The Discrete p-Maxian Location Problem. Comput. and Opns. Res. 17, 51-61.

Digital Library

[9]

GAREY, M. R., AND D. S. JOHNSON. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness . W. H. Freeman, San Francisco.

[10]

HANDLER, G. Y., AND P. B. MIRCHANDANI. 1979. Location on Networks: Theory and Algorithms. MIT Press, Cambridge, Mass.

[11]

HANSEN, P., AND I. D. MOON. 1988. Dispersing Facilities on a Network. Presentation at the TIMS/ORSA Joint National Meeting, Washington, D.C.

[12]

HOROWITZ, E., AND S. SAHNI. 1984. Fundamentals of Computer Algorithms. Computer Science Press, Rockville, Maryland.

[13]

KUBY, M. J. 1987. Programming Models for Facility Dispersion: The p-Dispersion and Maxisum Dispersion Problems. Geog. Anal. 19, 315-329.

[14]

MELACHRINOUDIS, E., AND T. P. CULLINANE. 1986. Locating an Undesirable Facility With a Minimax Criterion. Eur. J. Opnl. Res. 24, 239-246.

[15]

PREPARATA, F. P., AND SHAMOS, M. I. 1985. Computational Geometry: An Introduction. Springer-Verlag, New York.

Digital Library

[16]

ROBERTS, F. S. 1984. Applied Combinatorics. Prentice-Hall, Englewood Cliffs, New Jersey.

[17]

STEUER, R. E. 1986. Multiple Criteria Optimization: Theory and Application. John Wiley, New York.

[18]

TAMIR, A. 1991. Obnoxious Facility Location on Graphs. SIAM J. Disc. Math. 4, 550-567.

Digital Library

[19]

WHITE, D. J. 1991. The Maximal Dispersion Problem and the 'First Point Outside the Neighborhood' Heuristic. Comput. and Opns. Res. 18, 43-50.

Digital Library

[20]

WHITE, D. J. 1992. The Maximal Dispersion Problem. J. Applic. Math, in Bus. and Ind. (to appear).

[21]

WANG, D. W., AND Y. S. Kuo. 1988. A Study of Two Geometric Location Problems. Infor. Proc. Letts. 28, 281-286.

Digital Library

Cited By

Agarwal PEsmailpour AHu XSintos SYang J(2024)Computing A Well-Representative Summary of Conjunctive Query ResultsProceedings of the ACM on Management of Data10.1145/36958352:5(1-27)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695835
Kurkure YShamo MWiseman JGalhotra SSintos S(2024)Faster Algorithms for Fair Max-Min Diversification in RdProceedings of the ACM on Management of Data10.1145/36549402:3(1-26)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654940
Lanciano TMiyauchi AFazzone ABonchi F(2024)A Survey on the Densest Subgraph Problem and its VariantsACM Computing Surveys10.1145/365329856:8(1-40)Online publication date: 22-Mar-2024
https://dl.acm.org/doi/10.1145/3653298
Show More Cited By

Heuristic and Special Case Algorithms for Dispersion Problems

Recommendations

On Worst-Case to Average-Case Reductions for NP Problems

We show that if an NP-complete problem has a nonadaptive self-corrector with respect to any samplable distribution, then coNP is contained in NP/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow [SIAM J. Comput., 22 (...
On Worst-Case to Average-Case Reductions for NP Problems
FOCS '03: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science

We show that if an NP-complete problem has a non-adaptive self-corrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion ...
Hybrid heuristic algorithms for single machine total weighted tardiness scheduling problems

This paper addresses on solving a well known Non Polynomial (NP) hard type problem, namely the single machine total weighted-tardiness problem. The performances of three hybrid heuristic algorithms to solve the single machine scheduling problems with ...

Comments

Information & Contributors

Information

Published In

cover image Operations Research

Operations Research Volume 42, Issue 2

April 1994

205 pages

ISSN:0030-364X

Issue’s Table of Contents

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 April 1994

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

68
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 30 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Agarwal PEsmailpour AHu XSintos SYang J(2024)Computing A Well-Representative Summary of Conjunctive Query ResultsProceedings of the ACM on Management of Data10.1145/36958352:5(1-27)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695835
Kurkure YShamo MWiseman JGalhotra SSintos S(2024)Faster Algorithms for Fair Max-Min Diversification in RdProceedings of the ACM on Management of Data10.1145/36549402:3(1-26)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654940
Lanciano TMiyauchi AFazzone ABonchi F(2024)A Survey on the Densest Subgraph Problem and its VariantsACM Computing Surveys10.1145/365329856:8(1-40)Online publication date: 22-Mar-2024
https://dl.acm.org/doi/10.1145/3653298
Kumpulainen IAdriaens FTatti NBaeza-Yates RBonchi F(2024)Max-Min Diversification with Asymmetric DistancesProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671757(1440-1450)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671757
Li WZhou Y(2024)Locating Two Facilities on a Square with a Minimum Distance RequirementFrontiers of Algorithmics10.1007/978-981-97-7752-5_23(317-333)Online publication date: 30-Jul-2024
https://dl.acm.org/doi/10.1007/978-981-97-7752-5_23
Do AGuo MNeumann ANeumann FElkind E(2023)Diverse approximations for monotone submodular maximization problems with a matroid constraintProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/617(5558-5566)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/617
Hanaka TKiyomi MKobayashi YKobayashi YKurita KOtachi YWilliams BChen YNeville J(2023)A framework to design approximation algorithms for finding diverse solutions in combinatorial problemsProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i4.25511(3968-3976)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i4.25511
Amagata DWilliams BChen YNeville J(2023)Diversity maximization in the presence of outliersProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i10.26454(12338-12345)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i10.26454
Haqi AZarrabi-Zadeh HAgrawal KShun J(2023)Almost Optimal Massively Parallel Algorithms for k-Center Clustering and Diversity MaximizationProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591077(239-247)Online publication date: 17-Jun-2023
https://dl.acm.org/doi/10.1145/3558481.3591077
Ohsaka NTogashi RChen HDuh WHuang HKato MMothe JPoblete B(2023)A Critical Reexamination of Intra-List Distance and DispersionProceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval10.1145/3539618.3591623(1619-1628)Online publication date: 19-Jul-2023
https://dl.acm.org/doi/10.1145/3539618.3591623
Show More Cited By

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents