Statistics Papers

Document Type

Technical Report

Date of this Version

6-2017

Publication Source

Computational Geometry

Volume

63

Start Page

53

Last Page

62

DOI

10.1016/j.comgeo.2017.02.003

Abstract

In this paper we study the last round of the discrete Voronoi game in ℝ2, a problem which is also of independent interest in competitive facility location. The game consists of two players P1 and P2, and a finite set U of users in the plane. The players have already placed two disjoint sets of facilities F and S, respectively, in the plane. The game begins with P1 placing a new facility followed by P2 placing another facility, and the objective of both the players is to maximize their own total payoffs. In this paper we propose polynomial time algorithms for determining the optimal strategies of both the players for arbitrarily located existing facilities F and S. We show that in the L1 and the L metrics, the optimal strategy of P2, given any placement of P1, can be found in O(n log n) time, and the optimal strategy of P1 can be found in O(n5 log n) time. In the L2 metric, the optimal strategies of P2 and P1 can be obtained in O(n2) and O(n2) and O(n8) times, respectively.

Copyright/Permission Statement

© 2017 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

competitive facility location, geometric depth, Voronoi diagram

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Date Posted: 25 October 2018

This document has been peer reviewed.