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Improved complexity results for several multifacility location problems on trees

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  • Jörg Kalcsics

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

Suggested Citation

  • Jörg Kalcsics, 2011. "Improved complexity results for several multifacility location problems on trees," Annals of Operations Research, Springer, vol. 191(1), pages 23-36, November.
    • Handle: RePEc:spr:annopr:v:191:y:2011:i:1:p:23-36:10.1007/s10479-011-0905-4
    DOI: 10.1007/s10479-011-0905-4
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