Consensus and mutual exclusion in a multiple access channel

Jurek Czyzowicz, Leszek Ga̧sieniec, Dariusz R. Kowalski, Andrzej Pelc

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

We consider deterministic feasibility and time complexity of two fundamental tasks in distributed computing: consensus and mutual exclusion. Processes have different labels and communicate through a multiple access channel. The adversary wakes up some processes in possibly different rounds. In any round every awake process either listens or transmits. The message of a process i is heard by all other awake processes, if i is the only process to transmit in a given round. If more than one process transmits simultaneously, there is a collision and no message is heard. We consider three characteristics that may or may not exist in the channel: collision detection (listening processes can distinguish collision from silence), the availablity of a global clock showing the round number, and the knowledge of the number n of all processes. If none of the above three characteristics is available in the channel, we prove that consensus and mutual exclusion are infeasible; if at least one of them is available, both tasks are feasible and we study their time complexity. Collision detection is shown to cause an exponential gap in complexity: if it is available, both tasks can be performed in time logarithmic in n, which is optimal, and without collision detection both tasks require linear time. We then investigate both consensus and mutual exclusion in the absence of collision detection, but under alternative presence of the two other features. With global clock, we give an algorithm whose time complexity linearly depends on n and on the wake-up time, and an algorithm whose complexity does not depend on the wake-up time and differs from the linear lower bound only by a factor O(log2 n). If n is known, we also show an algorithm whose complexity differs from the linear lower bound only by a factor O(log 2 n).

Original languageEnglish (US)
Title of host publicationDistributed Computing - 23rd International Symposium, DISC 2009, Proceedings
Pages512-526
Number of pages15
DOIs
StatePublished - Dec 1 2009
Externally publishedYes
Event23rd International Symposium on Distributed Computing, DISC 2009 - Elche, Spain
Duration: Sep 23 2009Sep 25 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5805 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Symposium on Distributed Computing, DISC 2009
CountrySpain
CityElche
Period9/23/099/25/09

Keywords

  • Collision detection
  • Consensus
  • Multiple access channel
  • Mutual exclusion

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Czyzowicz, J., Ga̧sieniec, L., Kowalski, D. R., & Pelc, A. (2009). Consensus and mutual exclusion in a multiple access channel. In Distributed Computing - 23rd International Symposium, DISC 2009, Proceedings (pp. 512-526). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5805 LNCS). https://doi.org/10.1007/978-3-642-04355-0_51