Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Competitive Strategy for Distance-Aware Online Shape Allocation   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.

20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: stat