Scalable Parallel Algorithms for FPT Problems

Abu-Khzam, Faisal N.; Langston, Michael A.; Shanbhag, Pushkar; Symons, Christopher T.

doi:10.1007/s00453-006-1214-1

Cited by 66 publications

(65 citation statements)

References 21 publications

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“…Therefore, CLIQUE parameterized by can be solved in O(1.28 k + n 2 ) time by constructing the complement graph and then using the currently best fixed-parameter algorithm for VERTEX COVER [22]. This approach, when combined with other techniques, such as the degeneracy-ordering described below, efficiently solves CLIQUE in biological, financial and social networks [23,24].…”

Section: The Clique Problem From the Viewpoint Of Multivariate Algorimentioning

confidence: 99%

Multivariate Algorithmics for Finding Cohesive Subnetworks

Komusiewicz

2016

Algorithms

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Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the detection of network communities. For each clique relaxation, we give an overview of basic model properties and of the complexity of the problem of finding large cohesive subgraphs under this model. Since this problem is usually NP-hard, we focus on combinatorial fixed-parameter algorithms exploiting typical structural properties of input networks.

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Section: The Clique Problem From the Viewpoint Of Multivariate Algorimentioning

confidence: 99%

Multivariate Algorithmics for Finding Cohesive Subnetworks

Komusiewicz

2016

Algorithms

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“…By avoiding the enumeration problems of maximal clique, it is also highly scalable. Moreover, through its complementary duality with vertex cover, it is amenable to advances in fixedparameter tractability [47]. Paraclique's main drawback is its use of multiple parameters, making algorithm tuning more challenging.…”

Section: Discussionmentioning

confidence: 99%

A Systematic Comparison of Genome Scale Clustering Algorithms

Jay

Eblen

Zhang

et al. 2011

Bioinformatics Research and Applications

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Background: A wealth of clustering algorithms has been applied to gene co-expression experiments. These algorithms cover a broad range of approaches, from conventional techniques such as k-means and hierarchical clustering, to graphical approaches such as k-clique communities, weighted gene co-expression networks (WGCNA) and paraclique. Comparison of these methods to evaluate their relative effectiveness provides guidance to algorithm selection, development and implementation. Most prior work on comparative clustering evaluation has focused on parametric methods. Graph theoretical methods are recent additions to the tool set for the global analysis and decomposition of microarray co-expression matrices that have not generally been included in earlier methodological comparisons. In the present study, a variety of parametric and graph theoretical clustering algorithms are compared using well-characterized transcriptomic data at a genome scale from Saccharomyces cerevisiae. Methods: For each clustering method under study, a variety of parameters were tested. Jaccard similarity was used to measure each cluster's agreement with every GO and KEGG annotation set, and the highest Jaccard score was assigned to the cluster. Clusters were grouped into small, medium, and large bins, and the Jaccard score of the top five scoring clusters in each bin were averaged and reported as the best average top 5 (BAT5) score for the particular method. Results: Clusters produced by each method were evaluated based upon the positive match to known pathways. This produces a readily interpretable ranking of the relative effectiveness of clustering on the genes. Methods were also tested to determine whether they were able to identify clusters consistent with those identified by other clustering methods.

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“…A recent approach of the latter kind that has proven useful in biological applications is the work of Abu-Khzam et al [3].…”

Section: Introductionmentioning

confidence: 99%

“…For example, finding a minimum vertex cover in a network corresponds to locating an optimal set of nodes on which to strategically place controllers such that they can monitor the data going through every link in the network. Algorithms for minimum vertex cover can also be used to solve the closely related problem of finding a maximum clique, which has a range of applications in biology, such as identifying related protein sequences [3].…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Local Search Approach to Vertex Cover

Richter

Helmert

Gretton

2007

Lecture Notes in Computer Science

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Abstract. We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used DIMACS benchmarks for the related clique problem, finding that our approach is competitive with the current best stochastic local search algorithm for finding cliques. On three very large problem instances, our algorithm establishes new records in solution quality.

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Scalable Parallel Algorithms for FPT Problems

Cited by 66 publications

References 21 publications

Multivariate Algorithmics for Finding Cohesive Subnetworks

Multivariate Algorithmics for Finding Cohesive Subnetworks

A Systematic Comparison of Genome Scale Clustering Algorithms

A Stochastic Local Search Approach to Vertex Cover

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