The communication complexity of distributed task allocation

Andrew Drucker, Fabian Kuhn, Rotem Oshman

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

Abstract

We consider a distributed task allocation problem in which m players must divide a set of n tasks between them. Each player i receives as input a set X i of tasks such that the union of all input sets covers the task set. The goal is for each player to output a subset Y i ⊆ X i, such that the outputs (Y 1,...,Y m) form a partition of the set of tasks. The problem can be viewed as a distributed one-shot variant of the well-known k-server problem, and we also show that it is closely related to the problem of finding a rooted spanning tree in directed broadcast networks. We study the communication complexity and round complexity of the task allocation problem. We begin with the classical two-player communication model, and show that the randomized communication complexity of task allocation is Ω(n), even when the set of tasks is known to the players in advance. For the multi-player setting with m = O(n) we give two upper bounds in the shared-blackboard model of communication. We show that the problem can be solved in O(log n) rounds and O(n log n) total bits for arbitrary inputs; moreover, if for any set X of tasks, there are at least α|X| players that have at least one task from X in their inputs, then O((1/α + log m)log n) rounds suffice even if each player can only write O(log n) bits on the blackboard in each round. Finally, we extend our results to the case where the players communicate over an arbitrary directed communication graph instead of a shared blackboard. As an application of these results, we also consider the related problem of constructing a directed spanning tree in strongly-connected directed networks and we show lower and upper bounds for that problem.

Original languageEnglish
Title of host publicationPODC'12 - Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing
Pages67-76
Number of pages10
DOIs
StatePublished - 2012
Externally publishedYes
Event2012 ACM Symposium on Principles of Distributed Computing, PODC'12 - Madeira, Portugal
Duration: 16 Jul 201218 Jul 2012

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference2012 ACM Symposium on Principles of Distributed Computing, PODC'12
Country/TerritoryPortugal
CityMadeira
Period16/07/1218/07/12

Keywords

  • directed spanning trees
  • multiparty communication complexity
  • task allocation
  • unidirectional links

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