Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and
  Minor-Free Graphs   A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself.

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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol