A distributed algorithm for finding all maximal cliques in a network graph

Jennings, Esther; Motyckova, Lenka

doi:10.1007/bfb0023836

Cited by 5 publications

(9 citation statements)

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“…Many algorithms for this problem are known; see, for example, Jennings and Motycková [1992], Johnson et al [1988], Lawler et al [1980], Leung [1984], Liang et al [1991], Makino and Uno [2004], Mishra and Pitt [1997], Stix [2004], Tsukiyama et al [1977], and Yu and Chen [1993], or the survey by Bomze et al [1999]. However, all take at least quadratic time per generated independent set even on sparse graphs.…”

Section: Introductionmentioning

confidence: 97%

All maximal independent sets and dynamic dominance for sparse graphs

Eppstein

2009

ACM Trans. Algorithms

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We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O( √ m) per update. We use the domination data structures as part of our enumeration algorithms.

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Section: Introductionmentioning

confidence: 97%

All maximal independent sets and dynamic dominance for sparse graphs

Eppstein

2009

ACM Trans. Algorithms

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“…1. a Agent network at time t = 1, b agent network at time t = 2, c agent network at time t = 3, d agent network at time t = 4, e agent network at time t = 8, f agent network at time t = 12, g agent network at time t = 16, h agent network at time t = 20 and t = 24 (4) ; c AVM (8) ; d AVM (12) ; e AVM (16) ; f AVM (20) ; g AVM (24) ; h AVM (28) areas) gradually disappear, while those within communities (the dots within the four dense areas) gradually increase. Finally, the agent network evolves into a new network containing four separated cliques, each of which corresponds to a community of the random network, as shown in Fig.…”

Section: Example 34mentioning

confidence: 99%

“…In the literature, there are some works related to ours in certain aspects, such as the methods of "distributed finding maximal cliques" [2,8] and "autonomously clustering sensor networks" [1,17,28]. In what follows, we will take a look at those related methods and compare them with ours.…”

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confidence: 99%

“…The objective of our method is to detect all communities of a given network defined by the linkage relationships among nodes, rather than the cliques defined as fully connected subgraphs or the clusters of sensor networks defined in terms of the spatial locations of nodes. (2) In addition, the problem solving mechanism adopted by our method, an AOC-based self-organization and self-aggregation paradigm [13][14][15], is completely distinct from those used by the above-mentioned methods, such as divide-and-conquer strategy [8], pheromone-based ACO system [2], self-declaration and self-pruning [1], asynchronous signaling [17], or quorum sensing [28].…”

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confidence: 99%

“…It is not expected to be a polynomial-time algorithm, and thus efforts have been made to come up with efficient approximations including parallel and/or distributed algorithms. For examples, Jennings and Motyskovd [8] have presented a distributed algorithm for finding the maximal clique in a graph, in which they adopted a divide-and-conquer strategy to recursively discover all "bipartite cliques" through message passing among distributed nodes. Bui and Rizzo [2] have provided a distributed ant colony optimization (ACO) algorithm to address this problem, where a group of ants work together to find an approximately maximal clique in a given network based on the local knowledge of each and a predefined pheromone distributing and sharing mechanism.…”

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confidence: 99%

See 2 more Smart Citations

An autonomy-oriented computing approach to community mining in distributed and dynamic networks

Yang

Liu

2009

Auton Agent Multi-Agent Syst

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A network community refers to a special type of network structure that contains a group of nodes connected based on certain relationships or similar properties. Our ability to mine communities hidden inside networks will readily enable us to effectively understand and exploit such networks. So far, various methods and algorithms have been developed to perform the task of community mining, where it is often required that the networks are processed in a centralized manner, and their structures will not dynamically change. However, in the real world, many applications involve distributed and dynamically evolving networks, in which resources and controls are not only decentralized but also updated frequently. It would be difficult for the existing methods to deal with these types of networks since their global topological representations are either not available or too hard to obtain due to their huge size, decentralization, and/or dynamic updates. The aim of our work is to address the problem of mining communities from a distributed and dynamic network. It differs from the previous ones in that here we introduce the notion of self-organizing agent networks, and provide an autonomy-oriented computing (AOC) approach to distributed and incremental mining of network communities. The AOC-based method utilizes reactive agents that can collectively detect and update community structures in a distributed and dynamically evolving network, based only on their local views and interactions. While providing detailed formulations, we present the results of our systematic validations using real-world benchmark networks as A preliminary, brief version of this work was presented as a regular paper at

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On computing all maximal cliques distributedly

Protti

França

Szwarcfiter

1997

Solving Irregularly Structured Problems in Parallel

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A distributed algorithm is presented for generating all maximal cIiques in a network graph, based on the sequential version of Tsukiyama et al. [TIAS77]. The time complexity of the proposed approach is restricted to the induced neighborhood of a node, and the communication complexity is O(md) where m is the number of connections, and d is the maximum degree in the graph. Messages are O(log n) bits long, where n is the number of nodes (processors) in the system. As an appIication, a distributed algorithm for constructing the clique graph k(G) from a given network graph G is developed within the scope of dynamic transformations of topologies.

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A distributed algorithm for finding all maximal cliques in a network graph

Cited by 5 publications

References 5 publications

All maximal independent sets and dynamic dominance for sparse graphs

All maximal independent sets and dynamic dominance for sparse graphs

An autonomy-oriented computing approach to community mining in distributed and dynamic networks

On computing all maximal cliques distributedly

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