### 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(log^{2} 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 language | English (US) |
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Title of host publication | Distributed Computing - 23rd International Symposium, DISC 2009, Proceedings |

Pages | 512-526 |

Number of pages | 15 |

DOIs | |

State | Published - Dec 1 2009 |

Externally published | Yes |

Event | 23rd International Symposium on Distributed Computing, DISC 2009 - Elche, Spain Duration: Sep 23 2009 → Sep 25 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5805 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd International Symposium on Distributed Computing, DISC 2009 |
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Country | Spain |

City | Elche |

Period | 9/23/09 → 9/25/09 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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

**Consensus and mutual exclusion in a multiple access channel.** / Czyzowicz, Jurek; Ga̧sieniec, Leszek; Kowalski, Dariusz R.; Pelc, Andrzej.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Distributed Computing - 23rd International Symposium, DISC 2009, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5805 LNCS, pp. 512-526, 23rd International Symposium on Distributed Computing, DISC 2009, Elche, Spain, 9/23/09. https://doi.org/10.1007/978-3-642-04355-0_51

}

TY - GEN

T1 - Consensus and mutual exclusion in a multiple access channel

AU - Czyzowicz, Jurek

AU - Ga̧sieniec, Leszek

AU - Kowalski, Dariusz R.

AU - Pelc, Andrzej

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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).

AB - 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).

KW - Collision detection

KW - Consensus

KW - Multiple access channel

KW - Mutual exclusion

UR - http://www.scopus.com/inward/record.url?scp=76649130169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76649130169&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04355-0_51

DO - 10.1007/978-3-642-04355-0_51

M3 - Conference contribution

AN - SCOPUS:76649130169

SN - 3642043542

SN - 9783642043543

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 512

EP - 526

BT - Distributed Computing - 23rd International Symposium, DISC 2009, Proceedings

ER -