Heuristic and Special Case Algorithms for Dispersion Problems

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 ( M...

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Bibliographic Details
Published in:Operations research Vol. 42; no. 2; pp. 299 - 310
Main Authors: Ravi, S. S, Rosenkrantz, D. J, Tayi, G. K
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.03.1994
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
analysis of algorithms: computational complexity
Applied sciences
Approximation algorithms
Dynamic programming
Exact sciences and technology
facilities/equipment planning: discrete location
Flows in networks. Combinatorial problems
Functions
Heuristic
Heuristics
Inequality
Integers
Mathematical theorems
Natural satellites
Operational research and scientific management
Operational research. Management science
Operations research
Optimal solutions
Optimization
Polynomials
programming: heuristic
Studies
Triangle inequalities
One dimensional model
Heuristic method
Two dimensional model
Facility
Algorithm
Computational complexity
Location problem
Dispersion
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary: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 /2 for the 2-dimensional MAX-AVG dispersion problem.
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.42.2.299