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Register a new userParallel Correlation Clustering on Big Graphs
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Added by
Dimitris S. Papailiopoulos
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Given a similarity graph between items, correlation clustering (CC) groups similar items together and dissimilar ones apart. One of the most popular CC algorithms is KwikCluster: an algorithm that serially clusters neighborhoods of vertices, and obtains a 3-approximation ratio. Unfortunately, KwikCluster in practice requires a large number of clustering rounds, a potential bottleneck for large graphs. We present C4 and ClusterWild!, two algorithms for parallel correlation clustering that run in a polylogarithmic number of rounds and achieve nearly linear speedups, provably. C4 uses concurrency control to enforce serializability of a parallel clustering process, and guarantees a 3-approximation ratio. ClusterWild! is a coordination free algorithm that abandons consistency for the benefit of better scaling; this leads to a provably small loss in the 3-approximation ratio. We provide extensive experimental results for both algorithms, where we outperform the state of the art, both in terms of clustering accuracy and running time. We show that our algorithms can cluster billion-edge graphs in under 5 seconds on 32 cores, while achieving a 15x speedup.
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Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering tasks. In this paper, we study the problem of correlation clustering in bounded arboricity graphs with respect to the Massively Parallel Computation (MPC) model. More specifically, we are given a complete graph where the edges are either positive or negative, indicating whether pairs of vertices are similar or dissimilar. The task is to partition the vertices into clusters with as few disagreements as possible. That is, we want to minimize the number of positive inter-cluster edges and negative intra-cluster edges. Consider an input graph $G$ on $n$ vertices such that the positive edges induce a $lambda$-arboric graph. Our main result is a 3-approximation ($textit{in expectation}$) algorithm to correlation clustering that runs in $mathcal{O}(log lambda cdot textrm{poly}(log log n))$ MPC rounds in the $textit{strongly sublinear memory regime}$. This is obtained by combining structural properties of correlation clustering on bounded arboricity graphs with the insights of Fischer and Noever (SODA 18) on randomized greedy MIS and the $texttt{PIVOT}$ algorithm of Ailon, Charikar, and Newman (STOC 05). Combined with known graph matching algorithms, our structural property also implies an exact algorithm and algorithms with $textit{worst case}$ $(1+epsilon)$-approximation guarantees in the special case of forests, where $lambda=1$.
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For parallel breadth first search (BFS) algorithm on large-scale distributed memory systems, communication often costs significantly more than arithmetic and limits the scalability of the algorithm. In this paper we sufficiently reduce the communication cost in distributed BFS by compressing and sieving the messages. First, we leverage a bitmap compression algorithm to reduce the size of messages before communication. Second, we propose a novel distributed directory algorithm, cross directory, to sieve the redundant data in messages. Experiments on a 6,144-core SMP cluster show our algorithm outperforms the baseline implementation in Graph500 by 2.2 times, reduces its communication time by 79.0%, and achieves a performance rate of 12.1 GTEPS (billion edge visits per second)
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