TY - GEN

T1 - Brief announcement

T2 - 2009 ACM Symposium on Principles of Distributed Computing, PODC'09

AU - Brakerski, Zvika

AU - Patt-Shamir, Boaz

PY - 2009

Y1 - 2009

N2 - Given an undirected graph and 0 ≤ ε ≤ 1, a set of nodes is called ε-near clique if all but an ε fraction of the pairs of nodes in the set have a link between them. We present a fast synchronous network algorithm that uses small messages and finds a near-clique. Specifically, we present a constant-time algorithm that finds, with constant probability of success, a linear size ε-near clique if there exists an ε 3-near clique of linear size in the graph. The algorithm uses messages of O(log n) bits. The failure probability can be reduced to n -Ω(1) in O(log n) time, and the algorithm also works if the graph contains a clique of size Ω(n/ log α log n) for some α ∈ (0, 1). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting.

AB - Given an undirected graph and 0 ≤ ε ≤ 1, a set of nodes is called ε-near clique if all but an ε fraction of the pairs of nodes in the set have a link between them. We present a fast synchronous network algorithm that uses small messages and finds a near-clique. Specifically, we present a constant-time algorithm that finds, with constant probability of success, a linear size ε-near clique if there exists an ε 3-near clique of linear size in the graph. The algorithm uses messages of O(log n) bits. The failure probability can be reduced to n -Ω(1) in O(log n) time, and the algorithm also works if the graph contains a clique of size Ω(n/ log α log n) for some α ∈ (0, 1). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting.

KW - Clique

KW - Communication networks

KW - Property testing

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=70350637324&partnerID=8YFLogxK

U2 - 10.1145/1582716.1582790

DO - 10.1145/1582716.1582790

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AN - SCOPUS:70350637324

SN - 9781605583969

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

SP - 324

EP - 325

BT - PODC'09 - Proceedings of the 2009 ACM Symposium on Principles of Distributed Computing

Y2 - 10 August 2009 through 12 August 2009

ER -