A Parameterized Approximation Algorithm for the Multiple Allocation k-Hub Center

0Citations
Citations of this article
1Readers
Mendeley users who have this article in their library.
Get full text

Abstract

In the Multiple Allocation k -Hub Center, we are given a connected edge-weighted graph G, sets of clients C and hub locations H, where V(G) = C∪ H, a set of demands D⊆ C2 and a positive integer k. A solution is a set of hubs H⊆ H of size k such that every demand (a, b) is satisfied by a path starting in a, going through some vertex of H, and ending in b. The objective is to minimize the largest length of a path. We show that finding a (3 - ϵ) -approximation is NP-hard already for planar graphs. For arbitrary graphs, the approximation lower bound holds even if we parameterize by k and the value r of an optimal solution. An exact FPT algorithm is also unlikely when the parameter combines k and various graph widths, including pathwidth. To confront these hardness barriers, we give a (2 + ϵ) -approximation algorithm parameterized by treewidth, and, as a byproduct, for unweighted planar graphs, we give a (2 + ϵ) -approximation algorithm parameterized by k and r. Compared to classical location problems, computing the length of a path depends on non-local decisions. This turns standard dynamic programming algorithms impractical, thus our algorithm approximates this length using only local information.

Cite

CITATION STYLE

APA

Benedito, M. P. L., Melo, L. P., & Pedrosa, L. L. C. (2022). A Parameterized Approximation Algorithm for the Multiple Allocation k-Hub Center. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13568 LNCS, pp. 141–156). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20624-5_9

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free