5,070 research outputs found
A Much Faster Algorithm for Finding a Maximum Clique
We present improvements to a branch-and-bound maximumclique-finding algorithm MCS (WALCOM 2010, LNCS 5942, pp. 191–203) that was shown to be fast. First, we employ an efficient approximation algorithm for finding a maximum clique. Second, we make use of appropriate sorting of vertices only near the root of the search tree. Third, we employ a lightened approximate coloring mainly near the leaves of the search tree. A new algorithm obtained from MCS with the above improvements is named MCT. It is shown that MCT is much faster than MCS by extensive computational experiments. In particular, MCT is shown to be faster than MCS for gen400 p0.9 75 and gen400 p0.9 65 by over 328,000 and 77,000 times, respectively
Shared-Memory Parallel Maximal Clique Enumeration
We present shared-memory parallel methods for Maximal Clique Enumeration
(MCE) from a graph. MCE is a fundamental and well-studied graph analytics task,
and is a widely used primitive for identifying dense structures in a graph. Due
to its computationally intensive nature, parallel methods are imperative for
dealing with large graphs. However, surprisingly, there do not yet exist
scalable and parallel methods for MCE on a shared-memory parallel machine. In
this work, we present efficient shared-memory parallel algorithms for MCE, with
the following properties: (1) the parallel algorithms are provably
work-efficient relative to a state-of-the-art sequential algorithm (2) the
algorithms have a provably small parallel depth, showing that they can scale to
a large number of processors, and (3) our implementations on a multicore
machine shows a good speedup and scaling behavior with increasing number of
cores, and are substantially faster than prior shared-memory parallel
algorithms for MCE.Comment: 10 pages, 3 figures, proceedings of the 25th IEEE International
Conference on. High Performance Computing, Data, and Analytics (HiPC), 201
Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage
We propose a fast, parallel maximum clique algorithm for large sparse graphs
that is designed to exploit characteristics of social and information networks.
The method exhibits a roughly linear runtime scaling over real-world networks
ranging from 1000 to 100 million nodes. In a test on a social network with 1.8
billion edges, the algorithm finds the largest clique in about 20 minutes. Our
method employs a branch and bound strategy with novel and aggressive pruning
techniques. For instance, we use the core number of a vertex in combination
with a good heuristic clique finder to efficiently remove the vast majority of
the search space. In addition, we parallelize the exploration of the search
tree. During the search, processes immediately communicate changes to upper and
lower bounds on the size of maximum clique, which occasionally results in a
super-linear speedup because vertices with large search spaces can be pruned by
other processes. We apply the algorithm to two problems: to compute temporal
strong components and to compress graphs.Comment: 11 page
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