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arXiv · 1304.5971

A Competitive Strategy for Distance-Aware Online Shape Allocation

Sándor P. Fekete·Nils Schweer·Jan-Marc Reinhardt
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Abstract

We consider the following online allocation problem: Given a unit square S, and a sequence of numbers n_i between 0 and 1, with partial sum bounded by 1; at each step i, select a region C_i of previously unassigned area n_i in S. The objective is to make these regions compact in a distance-aware sense: minimize the maximum (normalized) average Manhattan distance between points from the same set C_i. Related location problems have received a considerable amount of attention; in particular, the problem of determining the "optimal shape of a city", i.e., allocating a single n_i has been studied. We present an online strategy, based on an analysis of space-filling curves; for continuous shapes, we prove a factor of 1.8092, and 1.7848 for discrete point sets.

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Sándor P. Fekete, Nils Schweer, Jan-Marc Reinhardt. 2013-04-22. A Competitive Strategy for Distance-Aware Online Shape Allocation. https://arxiv.org/abs/1304.5971

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