Distributed Discovery of Large Near-Cliques
Abstract
Given an undirected graph and $0\le\epsilon\le1$, a set of nodes is called $\epsilon$-near clique if all but an $\epsilon$ fraction of the pairs of nodes in the set have a link between them. In this paper 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 $\epsilon$-near clique if there exists an $\epsilon^3$-near clique of linear size in the graph. The algorithm uses messages of $O(\log n)$ bits. The failure probability can be reduced to $n^{-\Omega(1)}$ in $O(\log n)$ time, and the algorithm also works if the graph contains a clique of size $\Omega(n/\log^{\alpha}\log n)$ for some $\alpha \in (0,1)$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2009
- DOI:
- 10.48550/arXiv.0905.4147
- arXiv:
- arXiv:0905.4147
- Bibcode:
- 2009arXiv0905.4147B
- Keywords:
-
- Computer Science - Distributed;
- Parallel;
- and Cluster Computing;
- C.2.4;
- F.2.2;
- G.2.2