Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locating a robber with multiple probes   We consider a game in which a cop searches for a moving robber on a connected
graph using distance probes, which is a slight variation on one introduced by
Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any
$n$-vertex graph $G$ there is a winning strategy for the cop on the graph
$G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if
$m\geq n$. The present authors showed that, for all but a few small values of
$n$, this bound may be improved to $m\geq n/2$, which is best possible. In this
paper we consider the natural extension in which the cop probes a set of $k$
vertices, rather than a single vertex, at each turn. We consider the
relationship between the value of $k$ required to ensure victory on the
original graph and the length of subdivisions required to ensure victory with
$k=1$. We give an asymptotically best-possible linear bound in one direction,
but show that in the other direction no subexponential bound holds. We also
give a bound on the value of $k$ for which the cop has a winning strategy on
any (possibly infinite) connected graph of maximum degree $\Delta$, which is
best possible up to a factor of $(1-o(1))$.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci