Applying Modular Decomposition to Parameterized Bicluster Editing

Protti, Fábio; Silva, Maise Dantas da; Szwarcfiter, Jayme Luiz

doi:10.1007/11847250_1

Cited by 16 publications

(11 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Amit [1] proved the N P-hardness of the BGEP via a polynomial reduction from the 3-Exact 3-Cover Problem; in the same work, a binary integer programming formulation and an 11-approximation algorithm based on the relaxation of a linear program are described. Protti et al [8] proposed an algorithm for the parameterized version of the BGEP that uses a strategy based on modular decomposition techniques. Guo et al [9] developed a randomized 4-approximation algorithm for the BGEP.…”

Section: Introductionmentioning

confidence: 99%

On solving manufacturing cell formation via Bicluster Editing

Pinheiro

Martins

Protti

et al. 2016

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

This work investigates the Bicluster Graph Editing Problem (BGEP) and how it can be applied to solve the Manufacturing Cell Formation Problem (MCFP). We develop an exact method for the BGEP that consists of a Branch-and-Cut approach combined with a special separation algorithm based on dynamic programming. We also describe a new preprocessing procedure for the BGEP derived from theoretical results on vertex distances in the input graph. Computational experiments performed on randomly generated instances with various levels of difficulty show that our separation algorithm accelerates the convergence speed, and our preprocessing procedure is effective for low density instances. Other contribution of this work is to reveal the similarities between the BGEP and the MCFP. We show that the BGEP and the MCFP have the same solution space. This fact leads to the proposal of two new exact approaches for the MCFP based on mathematical formulations for the BGEP. Both approaches use the grouping efficacy measure as the objective function. Up to the authors' knowledge, these are the first exact methods that employ such a measure to optimally solve instances of the MCFP. The first approach consists of iteratively running several calls to a parameterized version of the BGEP, and the second is a linearization of a new fractional-linear model for the MCFP. Computational experiments performed on instances of the MCFP found in the literature show that our exact methods for the MCFP are able to prove several previously unknown optima.

show abstract

Section: Introductionmentioning

confidence: 99%

On solving manufacturing cell formation via Bicluster Editing

Pinheiro

Martins

Protti

et al. 2016

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…F. Protti et al [3] developed an algorithm that finished in (4 + | | + | |) for the unweighted version of bi-cluster editing. Later J. Guo et al [4] improved the running time to (3.24 + | |), by developing an improved branching strategy.…”

Section: Previous Studies and Resultsmentioning

confidence: 99%

Integrated simultaneous analysis of different biomedical data types with exact weighted bi-cluster editing

Sun

Guo

Baumbach

2012

Journal of Integrative Bioinformatics

View full text Add to dashboard Cite

SummaryThe explosion of biological data has largely influenced the focus of today's biology research. Integrating and analysing large quantity of data to provide meaningful insights has become the main challenge to biologists and bioinformaticians. One major problem is the combined data analysis of data from different types, such as phenotypes and genotypes. This data is modelled as bi-partite graphs where nodes correspond to the different data points, mutations and diseases for instance, and weighted edges relate to associations between them. Bi-clustering is a special case of clustering designed for partitioning two different types of data simultaneously. We present a bi-clustering approach that solves the NP-hard weighted bi-cluster editing problem by transforming a given bi-partite graph into a disjoint union of bi-cliques. Here we contribute with an exact algorithm that is based on fixed-parameter tractability. We evaluated its performance on artificial graphs first. Afterwards we exemplarily applied our Java implementation to data of genome-wide association studies (GWAS) data aiming for discovering new, previously unobserved geno-to-pheno associations. We believe that our results will serve as guidelines for further wet lab investigations. Generally our software can be applied to any kind of data that can be modelled as bi-partite graphs. To our knowledge it is the fastest exact method for weighted bi-cluster editing problem.

show abstract

“…The fixed-parameter tractability of the Cluster Editing problem (for ordinary non-fuzzy graphs) has been shown, with a series of improvements in [8,19,28], when using the editing cost k as parameter. The problem has also been shown to admit a linear kernelization [15,21].…”

Section: Introductionmentioning

confidence: 98%

Clustering with partial information

Bodlaender

Fellows

Heggernes

et al. 2010

Theoretical Computer Science

View full text Add to dashboard Cite

a b s t r a c tThe Correlation Clustering problem, also known as the Cluster Editing problem, seeks to edit a given graph by adding and deleting edges to obtain a collection of vertex-disjoint cliques, such that the editing cost is minimized. The Edge Clique Partitioning problem seeks to partition the edges of a given graph into edge-disjoint cliques, such that the number of cliques is minimized. Both problems are known to be NP-hard, and they have been previously studied with respect to approximation and fixed-parameter tractability. In this paper we study these two problems in a more general setting that we term fuzzy graphs, where the input graphs may have missing information, meaning that whether or not there is an edge between some pairs of vertices of the input graph can be undecided.For fuzzy graphs the Correlation Clustering and Edge Clique Partitioning problems have previously been studied only with respect to approximation. Here we give parameterized algorithms based on kernelization for both problems. We prove that the Correlation Clustering problem is fixed-parameter tractable on fuzzy graphs when parameterized by (k, r), where k is the editing cost and r is the minimum number of vertices required to cover the undecided edges. In particular we show that it has a polynomial-time reduction to a problem kernel on O(k 2 + r) vertices. We provide an analogous result for the Edge Clique Partitioning problem on fuzzy graphs. Using (k, r) as parameters, where k bounds the size of the partition, and r is the minimum number of vertices required to cover the undecided edges, we describe a polynomial-time kernelization to a problem kernel on O(k 4 · 3 r ) vertices. This implies fixed-parameter tractability for this parameterization.Furthermore we also show that parameterizing only by the number of cliques k, is not enough to obtain fixed-parameter tractability. The problem remains, in fact, NP-hard for each fixed k > 2.

show abstract

Applying Modular Decomposition to Parameterized Bicluster Editing

Cited by 16 publications

References 13 publications

On solving manufacturing cell formation via Bicluster Editing

On solving manufacturing cell formation via Bicluster Editing

Integrated simultaneous analysis of different biomedical data types with exact weighted bi-cluster editing

Clustering with partial information

Contact Info

Product

Resources

About