Time Complexity of the Ageev’s Algorithm to Solve the Uniform Hard Capacities Facility Location Problem
We show that the facility location problem with uniform hard capacities can be solved by the Ageev’s algorithm in \(O(m^3n^2)\) time, where m is the number of facilities and n is the number of clients. This improves the results \(O(m^5 n^2)\) of Ageev in 2004 and \(O(m^4n^2)\) of Ageev, Gimadi, and Kurochkin in 2009.
KeywordsFacility location problem Capacitated Uniform Network Path graph Exact algorithm Dynamic programming technique Polynomial Time complexity
Sections 1 and 2 of this research were supported by the Russian Foundation for Basic Research (project 16-07-00168), by the Russian Ministry of Science and Education under the 5–100 Excellence Programme and by the program of fundamental scientific researches of the SB RAS I.5.1. Section 3 is supported by the Russian Science Foundation (project 16-11-10041).
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