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.
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Kalcsics, J. Improved complexity results for several multifacility location problems on trees. Ann Oper Res 191, 23–36 (2011). https://doi.org/10.1007/s10479-011-0905-4
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DOI: https://doi.org/10.1007/s10479-011-0905-4