Elsevier

Theoretical Computer Science

Volume 555, 23 October 2014, Pages 43-54
Theoretical Computer Science

A competitive strategy for distance-aware online shape allocation

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Abstract

We consider the following online allocation problem: Given a unit square S, and a sequence of numbers ni[0,1] with j=0inj1; at each step i, select a region Ci of previously unassigned area ni 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 Ci. 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 ni 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.

Keywords

Clustering
Average distance
Online problems
Optimal shape of a city
Space-filling curves
Competitive analysis

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