Parallel algorithms for finding cliques in a graph
01 Jan 2011-Vol. 268, Iss: 1, pp 012030
TL;DR: The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems and suggest practical guide lines to inspect a given graph before starting a large scale search.
Abstract: A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.
Citations
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31 Dec 1994
TL;DR: A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement and Computational results for an efficient implementation on an IBM 3090 computer are provided.
Abstract: We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.
467 citations
21 Sep 2015
TL;DR: Preliminary results for a fast parallel adaptation of the well-known k-means clustering algorithm to graphs are presented and this method is going to be used to detect communities in complex networks.
Abstract: In this paper we present preliminary results for afast parallel adaptation of the well-known k-means clusteringalgorithm to graphs. We are going to use our method to detectcommunities in complex networks. For testing purposes we willuse the graph generator of Lancichinetti et al., and we aregoing to compare our method with the OSLOM, CPM, and hubpercolation overlapping community detection methods.
6 citations
Cites methods from "Parallel algorithms for finding cli..."
...Traditionally k-means is applied in a graph theoretic approach in a two-step fashion [16], [2], [12]....
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27 Jul 2014
TL;DR: This paper proposes and discusses an efficient custom instruction set identification method and corresponding automatic tool for multi-issue VLIW ASIPs, which search for the common operation patterns of the most frequently executed basic blocks of a given application, with different sizes and shapes.
Abstract: Custom Instruction Identification is an important part in the design of efficient Application-Specific Processors (ASIPs). It consists of profiling of a given application to find patterns of basic operations that are frequently executed. Operations of such patterns can be implemented together as a single custom instruction to speedup the execution of the application. Because of the problem's high complexity, several methods have been proposed for specific single-issue (RISC) processors and architectures, limiting the shape and size of custom instructions that can actually be identified and, possibly, implemented. In this paper, we propose and discuss an efficient custom instruction set identification method and corresponding automatic tool for multi-issue VLIW ASIPs, which search for the common operation patterns of the most frequently executed basic blocks of a given application, with different sizes and shapes. The speedup results for the custom instructions identified by our tool are provided for a set of benchmark applications. The speedup is up to 68%, with only a few custom instructions used.
5 citations
Cites background from "Parallel algorithms for finding cli..."
...The clique-finding problem is analogous to the sub-graph isomorphism problem and is also known to be NP-Complete, but with existing heuristics [16] and parallel solutions [17]–[19] that try to reduce the cliquefinding execution time....
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TL;DR: A family of further benchmark problems is proposed mainly to test exhaustive clique search procedures to assess the performance of practical exactClique search algorithms.
Abstract: There are well established widely used benchmark tests to assess the performance of practical exact clique search algorithms. In this paper a family of further benchmark problems is proposed mainly to test exhaustive clique search procedures.
4 citations
Cites background from "Parallel algorithms for finding cli..."
...In order to find bounds for ω(G) the following node coloring was proposed in [21]....
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08 Jun 2015
TL;DR: The variant of the Monte Carlo method, the Las Vegas method can be used for overcoming some special barriers that can occur in the course of dividing such problems as maximum clique and k-clique.
Abstract: In this paper we introduce a new method for speeding up parallel run times of discrete optimization problems which can be used for different problems. We propose that the variant of the Monte Carlo method, the Las Vegas method can be used for overcoming some special barriers that can occur in the course of dividing such problems. Especially the problem of maximum clique and k-clique is examined, and the new algorithm with the relevant measurements is presented.
4 citations
References
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TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,065 citations
TL;DR: A branch-and-bound algorithm for the maximum clique problem--which is computationally equivalent to the maximum independent (stable) set problem--is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy.
645 citations
TL;DR: In this paper, a partially enumerative algorithm for the maximum clique problem is presented, which is very simple to implement on an IBM 3090 computer and can be used to generate graphs with up to 3000 vertices and over one million edges.
476 citations
31 Dec 1994
TL;DR: A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement and Computational results for an efficient implementation on an IBM 3090 computer are provided.
Abstract: We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.
467 citations
"Parallel algorithms for finding cli..." refers background in this paper
...(The description of the algorithm with a complete program can be found in [11]....
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...(See for example [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]....
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Book•
01 Oct 1996
TL;DR: Addressed here are three difficult combinatorial optimization problems: finding cliques in a graph, colouring the vertices of a graphs, and solving instances of the satisfiability problem.
Abstract: The purpose of a DIMACS Challenge is to encourage and coordinate research in the experimental analysis of algorithms. The First DIMACS Challenge encouraged experimental work in the area of network flow and matchings. This Second DIMACS Challenge, on which this volume is based, took place in conjunction with the DIMACS Special Year on Combinatorial Optimization. Addressed here are three difficult combinatorial optimization problems: finding cliques in a graph, colouring the vertices of a graph, and solving instances of the satisfiability problem. These problems were chosen both for their practical interest and because of their theoretical intractability.
355 citations