Annals of Operations Research

, Volume 191, Issue 1, pp 23–36 | Cite as

Improved complexity results for several multifacility location problems on trees

Article
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Abstract

In this paper we consider multifacility location problems on tree networks. On general networks, these problems are usually NP-hard. On tree networks, however, often polynomial time algorithms exist; e.g., for the median, center, centdian, or special cases of the ordered median problem. We present an enhanced dynamic programming approach for the ordered median problem that has a time complexity of just O(ps 2 n 6) for the absolute and O(ps 2 n 2) for the node restricted problem, improving on the previous results by a factor of O(n 3). (n and p being the number of nodes and new facilities, respectively, and s (≤n) a value specific for the ordered median problem.) The same reduction in complexity is achieved for the multifacility k-centrum problem leading to O(pk 2 n 4) (absolute) and O(pk 2 n 2) (node restricted) algorithms.

Keywords

Multifacility location problems Dynamic programming Tree networks Ordered median problem 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of TechnologyKarlsruheGermany

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