Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mutual Search   We introduce a search problem called ``mutual search'' where $k$ \agents,
arbitrarily distributed over $n$ sites, are required to locate one another by
posing queries of the form ``Anybody at site $i$?''. We ask for the least
number of queries that is necessary and sufficient. For the case of two \agents
using deterministic protocols we obtain the following worst-case results: In an
oblivious setting (where all pre-planned queries are executed) there is no
savings: $n-1$ queries are required and are sufficient. In a nonoblivious
setting we can exploit the paradigm of ``no news is also news'' to obtain
significant savings: in the synchronous case $0.586n$ queries suffice and
$0.536n$ queries are required; in the asynchronous case $0.896n$ queries
suffice and a fortiori 0.536 queries are required; for $o(\sqrt{n})$ \agents
using a deterministic protocol less than $n$ queries suffice; there is a simple
randomized protocol for two \agents with worst-case expected $0.5n$ queries and
all randomized protocols require at least $0.125n$ worst-case expected queries.
The graph-theoretic framework we formulate for expressing and analyzing
algorithms for this problem may be of independent interest.

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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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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: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys