Abstract
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.
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Fekete, S.P., Schweer, N., Reinhardt, JM. (2013). A Competitive Strategy for Distance-Aware Online Shape Allocation. In: Ghosh, S.K., Tokuyama, T. (eds) WALCOM: Algorithms and Computation. WALCOM 2013. Lecture Notes in Computer Science, vol 7748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36065-7_6
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DOI: https://doi.org/10.1007/978-3-642-36065-7_6
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