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Parallel NC‐algorithms for multifacility location problems with mutual communication and their applications
Author(s) -
Averbakh Igor,
Berman Oded
Publication year - 2002
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.10027
Subject(s) - minimax , computer science , tree (set theory) , algorithm , scheme (mathematics) , mathematical optimization , parametric statistics , theoretical computer science , mathematics , combinatorics , mathematical analysis , statistics
The generic problem studied is to locate p distinguishable facilities on a tree to satisfy upper‐bound constraints on distances between pairs of facilities, given that each facility must be located within its own feasible region, which is defined as a subtree of the tree. We present a parallel location scheme (PLS) for solving the problem that can be implemented as an NC‐algorithm. We also introduce parallel NC‐algorithms based on the PLS for the minimax versions of the problem, including the distance‐constrained p ‐center problem with mutual communication. Combining the PLS and the improved Megiddo's parametric technique, we develop strongly polynomial serial algorithms for the minimax problems; the algorithms have the best complexities currently available in the literature. Efficient parallel algorithms are given for obtaining optimal regions of the facilities. © 2002 Wiley Periodicals, Inc.