Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Search with no Coordination   We consider a parallel version of a classical Bayesian search problem. $k$
agents are looking for a treasure that is placed in one of the boxes indexed by
$\mathbb{N}^+$ according to a known distribution $p$. The aim is to minimize
the expected time until the first agent finds it. Searchers run in parallel
where at each time step each searcher can "peek" into a box. A basic family of
algorithms which are inherently robust is \emph{non-coordinating} algorithms.
Such algorithms act independently at each searcher, differing only by their
probabilistic choices. We are interested in the price incurred by employing
such algorithms when compared with the case of full coordination. We first show
that there exists a non-coordination algorithm, that knowing only the relative
likelihood of boxes according to $p$, has expected running time of at most
$10+4(1+\frac{1}{k})^2 T$, where $T$ is the expected running time of the best
fully coordinated algorithm. This result is obtained by applying a refined
version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in
STOC'16, which was designed for the context of linear parallel search.We then
describe an optimal non-coordinating algorithm for the case where the
distribution $p$ is known. The running time of this algorithm is difficult to
analyse in general, but we calculate it for several examples. In the case where
$p$ is uniform over a finite set of boxes, then the algorithm just checks boxes
uniformly at random among all non-checked boxes and is essentially $2$ times
worse than the coordinating algorithm.We also show simple algorithms for Pareto
distributions over $M$ boxes. That is, in the case where $p(x) \sim 1/x^b$ for
$0< b < 1$, we suggest the following algorithm: at step $t$ choose uniformly
from the boxes unchecked in ${1, . . . ,min(M, \lfloor t/\sigma\rfloor)}$,
where $\sigma = b/(b + k - 1)$. It turns out this algorithm is asymptotically
optimal, and runs about $2+b$ times worse than the case of full coordination.

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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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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: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con