TY - GEN
T1 - Breaking the Ω (n) barrier
T2 - 30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018
AU - Robinson, Peter
AU - Scheideler, Christian
AU - Setzer, Alexander
N1 - Funding Information:
This work was supported by the LMS/ Computer Science Scheme 7 Grant Ref No.: SC7-1516-11 and by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901) under Grant No.: GZ SFB 901/02. Peter Robinson acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).
Publisher Copyright:
© 2018 Association for Computing Machinery.
PY - 2018/7/11
Y1 - 2018/7/11
N2 - We study the consensus problem in a synchronous distributed system of n nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires Ω (n) rounds in an n-node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginning of the previous round and unlimited computational power, but is oblivious to the current state of the nodes. Our main contributions are randomized distributed algorithms that achieve consensus with high probability among all except a small constant fraction of the nodes (i.e., “almost-everywhere”) against a late adaptive adversary who can block up to ϵn nodes in each round, for a small constant ϵ > 0. Our first protocol achieves binary almost-everywhere consensus and also guarantees a decision on the majority input value, thus ensuring plurality consensus. We also present an algorithm that achieves the same time complexity for multi-value consensus. Both of our algorithms succeed in O(log n) rounds with high probability, thus showing an exponential gap to the Ω (n) lower bound of Ben-Or and Bar-Joseph for strongly adaptive crash-failure adversaries, which can be strengthened to Ω(n) when allowing the adversary to block nodes instead of permanently crashing them. Our algorithms are scalable to large systems as each node contacts only an (amortized) constant number of peers in each communication round. We show that our algorithms are optimal up to constant (resp. sub-logarithmic) factors by proving that every almost-everywhere consensus protocol takes Ω(logd n) rounds in the worst case, where d is an upper bound on the number of communication requests initiated per node in each round. We complement our theoretical results with an experimental evaluation of the binary almost-everywhere consensus protocol revealing a short convergence time even against an adversary blocking a large fraction of nodes.
AB - We study the consensus problem in a synchronous distributed system of n nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires Ω (n) rounds in an n-node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginning of the previous round and unlimited computational power, but is oblivious to the current state of the nodes. Our main contributions are randomized distributed algorithms that achieve consensus with high probability among all except a small constant fraction of the nodes (i.e., “almost-everywhere”) against a late adaptive adversary who can block up to ϵn nodes in each round, for a small constant ϵ > 0. Our first protocol achieves binary almost-everywhere consensus and also guarantees a decision on the majority input value, thus ensuring plurality consensus. We also present an algorithm that achieves the same time complexity for multi-value consensus. Both of our algorithms succeed in O(log n) rounds with high probability, thus showing an exponential gap to the Ω (n) lower bound of Ben-Or and Bar-Joseph for strongly adaptive crash-failure adversaries, which can be strengthened to Ω(n) when allowing the adversary to block nodes instead of permanently crashing them. Our algorithms are scalable to large systems as each node contacts only an (amortized) constant number of peers in each communication round. We show that our algorithms are optimal up to constant (resp. sub-logarithmic) factors by proving that every almost-everywhere consensus protocol takes Ω(logd n) rounds in the worst case, where d is an upper bound on the number of communication requests initiated per node in each round. We complement our theoretical results with an experimental evaluation of the binary almost-everywhere consensus protocol revealing a short convergence time even against an adversary blocking a large fraction of nodes.
KW - Adaptive adversary
KW - Almost-everywhere consensus
KW - Probabilistic analysis
KW - Randomized Algorithm
UR - http://www.scopus.com/inward/record.url?scp=85053484312&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85053484312&partnerID=8YFLogxK
U2 - 10.1145/3210377.3210399
DO - 10.1145/3210377.3210399
M3 - Conference contribution
AN - SCOPUS:85053484312
T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures
SP - 173
EP - 182
BT - SPAA 2018 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures
PB - Association for Computing Machinery
Y2 - 16 July 2018 through 18 July 2018
ER -