A Competitive Strategy for Distance-Aware Online Shape Allocation

  • Sándor P. Fekete
  • Nils Schweer
  • Jan-Marc Reinhardt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7748)


We consider the following online allocation problem: Given a unit square S, and a sequence of numbers n i  ∈ {0,1} with \(\sum_{j=0}^i n_j\leq 1\); 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, both in a continuous and a discrete setting. 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.


Clustering average distance online problems optimal shape of a city space-filling curves competitive analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sándor P. Fekete
    • 1
  • Nils Schweer
    • 1
  • Jan-Marc Reinhardt
    • 1
  1. 1.Department of Computer ScienceTU BraunschweigGermany

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