TY - GEN

T1 - Unbeatable set consensus via topological and combinatorial reasoning

AU - Castañeda, Armando

AU - Gonczarowski, Yannai A.

AU - Moses, Yoram

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/7/25

Y1 - 2016/7/25

N2 - The set consensus problem has played an important role in the study of distributed systems for over two decades. Indeed, the search for lower bounds and impossibility results for this problem spawned the topological approach to distributed computing, which has given rise to new techniques in the design and analysis of protocols. The design of efficient solutions to set consensus has also proven to be challenging. In the synchronous crash failure model, the literature contains a sequence of solutions to set consensus, each improving upon the previous ones. This paper presents an unbeatable protocol for nonuniform κ-set consensus in the synchronous crash failure model. This is an efficient protocol whose decision times cannot be improved upon. Moreover, the description of our protocol is extremely succinct. Proving unbeatability of this protocol is a nontrivial challenge. We provide two proofs for its unbeatability: one is a subtle constructive combinatorial proof, and the other is a topological proof of a new style. These two proofs provide new insight into the connection between topological reasoning and combinatorial reasoning about protocols, which has long been a subject of interest. In particular, our topological proof reasons in a novel way about subcomplexes of the protocol complex, and sheds light on an open question posed by Guerraoui and Pochon (2009). Finally, using the machinery developed in the design of this unbeatable protocol, we propose a protocol for uniform κ-set consensus that beats all known solutions by a large margin.

AB - The set consensus problem has played an important role in the study of distributed systems for over two decades. Indeed, the search for lower bounds and impossibility results for this problem spawned the topological approach to distributed computing, which has given rise to new techniques in the design and analysis of protocols. The design of efficient solutions to set consensus has also proven to be challenging. In the synchronous crash failure model, the literature contains a sequence of solutions to set consensus, each improving upon the previous ones. This paper presents an unbeatable protocol for nonuniform κ-set consensus in the synchronous crash failure model. This is an efficient protocol whose decision times cannot be improved upon. Moreover, the description of our protocol is extremely succinct. Proving unbeatability of this protocol is a nontrivial challenge. We provide two proofs for its unbeatability: one is a subtle constructive combinatorial proof, and the other is a topological proof of a new style. These two proofs provide new insight into the connection between topological reasoning and combinatorial reasoning about protocols, which has long been a subject of interest. In particular, our topological proof reasons in a novel way about subcomplexes of the protocol complex, and sheds light on an open question posed by Guerraoui and Pochon (2009). Finally, using the machinery developed in the design of this unbeatable protocol, we propose a protocol for uniform κ-set consensus that beats all known solutions by a large margin.

KW - Optimality

KW - Topology; knowledge

KW - Unbeatability

KW - Uniform κ-set consensus

KW - κ-set consensus

UR - http://www.scopus.com/inward/record.url?scp=84984706246&partnerID=8YFLogxK

U2 - 10.1145/2933057.2933120

DO - 10.1145/2933057.2933120

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AN - SCOPUS:84984706246

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 107

EP - 116

BT - PODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 35th ACM Symposium on Principles of Distributed Computing, PODC 2016

Y2 - 25 July 2016 through 28 July 2016

ER -