HEURISTIC AND SPECIAL CASE ALGORITHMS FOR DISPERSION PROBLEMS
成果类型：
Article
署名作者：
RAVI, SS; ROSENKRANTZ, DJ; TAYI, GK
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.42.2.299
发表日期：
1994
页码：
299-310
关键词：
摘要：
The dispersion problem arises in selecting facilities to maximize som, 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 pi/2 for the 2-dimensional MAX-AVG dispersion problem.