Approximation algorithms for the stochastic priority facility location problem

Abstract

In this article, we present a primal-dual 3-approximation algorithm for the stochastic priority facility location problem. Combined with greedy augmentation procedure, such performance factor is further improved to 1.8526.

An approximation algorithm for k-median with priorities

“…2−τ }V (G f ) (see Appendix E for the proof). Using Lemmas 1 and 3, we know that our solution is a (max{6, 9+3τ 2−τ } + O(ǫ))-approximation solution to k-MP for case (2). Recall that G 1 is a 1 τ 3 + O(ǫ) -approximation solution to k-MP for case (1).…”

“…We can assume that |H 2 | > k for case (2). Otherwise we can convert G 2 to a feasible solution to LP1 by retaining only the highest priority opened at each facility.…”

“…Designing approximation algorithms for clustering with priorities remains an active area of research. For example, several constant factor approximation algorithms are known for the facility location objective [1][2][3]. Unfortunately, clustering with priorities remains elusive under the extensively studied k-median objective.…”

Distribution optimization of the specialized car repair store based on the maximization of market share

“…And then the improved algorithms for location problem were further studied. [16][17][18][19] The location problem is not only complex but also important, which can influence the routing problem, 20 the network design, 21 and even the traffic flow distribution. [22][23][24] Study on the competitive location problem was first proposed by Hotelling, 25 the core idea being that the customers choose the nearest facilities.…”