Improved complexity results for several multifacility location problems on trees

Jörg Kalcsics ()

Annals of Operations Research, 2011, vol. 191, issue 1, 23-36

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. Copyright Springer Science+Business Media, LLC 2011

Keywords: Multifacility location problems; Dynamic programming; Tree networks; Ordered median problem (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10479-011-0905-4

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