We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain R of normalized dimensions of 1 and ρ≥1, and distances are measured according to the Manhattan metric. We show that the family of 'balanced' facility configurations (in which the Voronoi cells of individual facilities are equalized with respect to a number of geometric properties) is considerably richer in this metric than for Euclidean distances. Our main result considers the 'One-Round Voronoi Game' with Manhattan distances, in which first player White and then player Black each place n points in R; each player scores the area for which one of its facilities is closer than the facilities of the opponent. We give a tight characterization: White has a winning strategy if and only if ρ≥n; for all other cases, we present a winning strategy for Black.
|Title of host publication||WALCOM: Algorithms and Computation|
|Subtitle of host publication||15th International Conference and Workshops, WALCOM 2021, Yangon, Myanmar, February 28 – March 2, 2021, Proceedings|
|Editors||Ryuhei Uehara, Seok-Hee Hong, Subhas C. Nandy|
|Number of pages||19|
|Publication status||E-pub ahead of print - 16 Feb 2021|
|Name||Lecture Notes in Computer Science |