Local distributed decision

Pierre Fraigniaud, Amos Korman, David Peleg

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

44 Scopus citations


A central theme in distributed network algorithms concerns understanding and coping with the issue of em locality. Despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems}. In the context of locality, solving a decision problem requires the processors to independently inspect their local neighborhoods and then collectively decide whether a given global input instance belongs to some specified language. We consider the standard LOCAL model of computation and define LD(t) (for local decision) as the class of decision problems that can be solved in t communication rounds. We first study the intriguing question of whether randomization helps in local distributed computing, and to what extent. Specifically, we define the corresponding randomized class BPLD(t,p,q), containing all languages for which there exists a randomized algorithm that runs in t rounds, accepts correct instances with probability at least p and rejects incorrect ones with probability at least q. We show that p 2+q = 1 is a threshold for the containment of LD(t) in BPLD(t,p,q). More precisely, we show that there exists a language that does not belong to LD(t) for any t=o(n) but does belong to BPLD(0,p,q) for any p,q ∈ (0,1] such that p 2+q ≤ 1. On the other hand, we show that, restricted to hereditary languages, BPLD(t,p,q) = LD(O(t)), for any function t and any p,q ∈ (0,1] such that p 2+q> 1. In addition, we investigate the impact of non-determinism on local decision, and establish some structural results inspired by classical computational complexity theory. Specifically, we show that non-determinism does help, but that this help is limited, as there exist languages that cannot be decided non-deterministically. Perhaps surprisingly, it turns out that it is the combination of randomization with non-determinism that enables to decide all languages in constant time. Finally, we introduce the notion of local reduction, and establish some completeness results.

Original languageEnglish
Title of host publicationProceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Number of pages10
StatePublished - 2011
Externally publishedYes
Event2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States
Duration: 22 Oct 201125 Oct 2011

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Country/TerritoryUnited States
CityPalm Springs, CA


  • local decision
  • local distributed algorithms
  • nondeterminism
  • oracles
  • randomized algorithms


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