Solving the maximum clique problem using PUBB

Shinano, Yuji; Fujie, Tetsuya; Ikebe, Yoshiko T.; Hirabayashi, Ryuichi

doi:10.1109/ipps.1998.669935

Cited by 9 publications

(4 citation statements)

References 11 publications

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“…Shinano et al demonstrated the effectiveness of parallelization of branch-and-bound algorithm for the maximum clique problem. 9 Pardalos et al, presented an original parallel algorithm for the maximum clique problem. 10 The authors described the parallelization of the Carraghan-Pardalos algorithm using the Message Passing Interface standard.…”

Section: Related Workmentioning

confidence: 99%

Recognizing Topological Analogy in Semantic Network

Trifunović

Stojković²,

Mišić³

et al. 2015

Int. J. Artif. Intell. Tools

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Recognizing topological analogy between the parts of semantic network seems to be very important step in the process of semantic categorization and interpretation of data that are embedded into the semantic network. Considering the semantic network as a set of graphs, recognition of topological analogy between the parts of semantic network can be treated as maximum common subgraph problem which falls in the group of exact graph matching problems. In this paper authors propose a new algorithm for maximum common subgraph detection aimed to a specific semantic network called Active Semantic Model (ASM). This semantic network can be represented as the set of labeled directed multigraphs with unique node labels. The structure of these graphs is specific because associations or edges are labeled with several attributes and some of them are related to nodes connected by edge. That kind of association-oriented structure enables associations or edges to play key role in the process of semantic categorization and interpretation of data. Furthermore, this kind of structure enables modeling semantic contexts in a form of semantically designated graphs (of associations). Proposed algorithm is capable of recognizing simultaneously maximum common subgraph of input graph and each of the graphs representing different contexts in ASM semantic network.Keywords: Graph matching; maximum common subgraph; labeled directed multigraph; topological analogy; active semantic model. Int. J. Artif. Intell. Tools 2015.24. Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 08/25/15. For personal use only.

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Section: Related Workmentioning

confidence: 99%

Recognizing Topological Analogy in Semantic Network

Trifunović

Stojković²,

Mišić³

et al. 2015

Int. J. Artif. Intell. Tools

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“…Parallel formulations of graph similarity computations have primarily focused on combinatorial methods aimed at identifying subgraph isomorphisms (or correspondingly, connected components in product graphs). Among these, the early efforts [1,48,57] utilize different parallel platforms (data parallel and messaging) for extracting isomorphic subgraphs or maximum cliques. For the special case of SimRank, for similarity computations within a single graph instance, [22] discuss an iterative aggregation technique exploiting the inherent parallelism and high memory bandwidth of graphics processing units (GPUs).…”

Section: Computing Graph Similaritiesmentioning

confidence: 99%

Fast parallel algorithms for graph similarity and matching

Κόλλιας¹,

Sathe²,

Schenk³

et al. 2014

Journal of Parallel and Distributed Computing

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With widespread availability of graph-structured data from sources ranging from social networks to biochemical processes, there is increasing need for efficient and effective graph analyses techniques. Graphs with millions of vertices and beyond are commonplace, necessitating both efficient serial algorithms, as well as scalable parallel formulations. This paper addresses the problem of global graph alignment on supercomputer-class clusters. Given two graphs (or two instances of the same graph), we define graph alignment as a mapping of each vertex in the first graph to a unique vertex in the second graph so as to optimize a given similarity-based cost function 1 . Graph alignment is typically implemented in two steps -in the first step, a similarity matrix is computed. Entries in the matrix quantify similarity of node pairs, one chosen from each graph. In the second step, similar vertices are extracted through a bipartite matching algorithm applied to the similarity matrix. Using a state of the art serial algorithm for similarity matrix computation called Network Similarity Decomposition (NSD), we derive corresponding parallel formulations. Coupling this parallel similarity algorithm with a parallel auction-based bipartite matching technique, we derive a complete graph matching pipeline that is highly efficient and scalable. We validate the performance of our integrated approach on a large, supercomputer-class cluster and diverse graph instances (including Protein Interaction (PPI) networks, Web graphs, and Wikipedia link structures). Experimental results demonstrate that our algorithms scale to large machine configurations and problem instances. (Ananth Grama) 1 In the sequel, we'll be using the word alignment as a synonym for global graph alignment; this is in contrast to local graph alignment that permits a vertex to have different pairings in feasible local alignments, making it an inherently ambiguous process Specifically, we show that our integrated pipeline enables the alignment of networks of sizes two orders of magnitude larger than currently possible (millions of vertices, tens of millions of edges).

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“…Thus, the authors showed empirically that the proposed algorithm achieves substantial performance improvements. In [12], Shinano et al have already shown that the success in combining the latest results for the maximal clique problem with DIMACS. Therefore, several improvements of DIMACS gave a significantly increased performance, even if the some increment procedure of the problem is much complex than the processing time base on the link used.…”

Section: Introductionmentioning

confidence: 99%

Solving the Graph Problem on the Maximal Clique Problem on the P-Systems with Mitochondria Enzymes Layer

Gaol

Matsuo

2019

Applied Sciences

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P systems with mitochondria enzymes layer computing is a recent version of P systems; it integrates a new feature inspired from the enzymes gate of a natural cell to the cell-like P systems. The model of a computational layer is well known as a problem of Non-Deterministic (NP-complete) in polynomial time. In this paper, we propose a P systems with enzymes to solve one of the most NP-hard problems, which is the determination of the maximal clique in a given undirected graph. In this context, the evolution strategy proposed is based on using objects under the control of enzymes placed on layers.

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Solving the maximum clique problem using PUBB

Cited by 9 publications

References 11 publications

Recognizing Topological Analogy in Semantic Network

Recognizing Topological Analogy in Semantic Network

Fast parallel algorithms for graph similarity and matching

Solving the Graph Problem on the Maximal Clique Problem on the P-Systems with Mitochondria Enzymes Layer

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