Parallel search with no coordination

Amos Korman, Yoav Rodeh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 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 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 + 1/k)2T,, 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) ~ 1/xb for 0 < b < 1, we suggest the following algorithm: at step t choose uniformly from the boxes unchecked in {1, …, min(M,⌊t/σ⌋)},, where σ = 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.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 24th International Colloquium, SIROCCO 2017, Revised Selected Papers
EditorsShantanu Das, Sebastien Tixeuil
PublisherSpringer Verlag
Number of pages17
ISBN (Print)9783319720494
StatePublished - 2017
Externally publishedYes
Event24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017 - Porquerolles, France
Duration: 19 Jun 201722 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10641 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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