Parallel exhaustive search without coordination

Pierre Fraigniaud, Amos Korman, Yoav Rodeh

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


We analyse parallel algorithms in the context of exhaustive search over totally ordered sets. Imagine an infinite list of "boxes", with a "treasure" hidden in one of them, where the boxes' order reflects the importance of finding the treasure in a given box. At each time step, a search protocol executed by a searcher has the ability to peek into one box, and see whether the treasure is present or not. Clearly, the best strategy of a single searcher would be to open the boxes one by one, in increasing order. Moreover, by equally dividing the workload between them, k searchers can trivially find the treasure k times faster than one searcher. However, this straightforward strategy is very sensitive to failures (e.g., crashes of processors), and overcoming this issue seems to require a large amount of communication. We therefore address the question of designing parallel search algorithms maximizing their speed-up and maintaining high levels of robustness, while minimizing the amount of resources for coordination. Based on the observation that algorithms that avoid communication are inherently robust, we focus our attention on identifying the best running time performance of non-coordinating algorithms. Specifically, we devise noncoordinating algorithms that achieve a speed-up of 9/8 for two searchers, a speed-up of 4/3 for three searchers, and in general, a speed-up of k/4 (1 + 1/k)2 for any k ≥ 1 searchers. Thus, asymptotically, the speed-up is only four times worse compared to the case of full coordination. Moreover, these bounds are tight in a strong sense as no non-coordinating search algorithm can achieve better speed-ups. Our algorithms are surprisingly simple and hence applicable. However they are memory intensive and so we suggest a practical, memory efficient version, with a speed-up of (k2-1)/4k. That is, it is only a factor of (k +1)/(k-1) slower than the optimal algorithm. Overall, we highlight that, in faulty contexts in which coordination between the searchers is technically difficult to implement, intrusive with respect to privacy, and/or costly in term of resources, it might well be worth giving up on coordination, and simply run our noncoordinating exhaustive search algorithms.

Original languageEnglish
Title of host publicationSTOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
EditorsYishay Mansour, Daniel Wichs
PublisherAssociation for Computing Machinery
Number of pages12
ISBN (Electronic)9781450341325
StatePublished - 19 Jun 2016
Externally publishedYes
Event48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States
Duration: 19 Jun 201621 Jun 2016

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© 2016 ACM.


  • Linear search
  • Non-coordination
  • Parallel computation
  • Robustness

ASJC Scopus subject areas

  • Software


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