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Parameterized complexity of generalized vertex cover problems
 In Proc. 9th WADS, volume 3608 of LNCS
, 2005
"... Abstract. Important generalizations of the Vertex Cover problem ..."
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Abstract. Important generalizations of the Vertex Cover problem
Parameterized Complexity of Vertex Cover Variants
, 2006
"... Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated Vertex Cover, and Maximum ..."
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Cited by 22 (5 self)
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Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated Vertex Cover, and Maximum
Simplicity is beauty: improved upper bounds for Vertex Cover
, 2005
"... Abstract — This paper presents an O(1.2738 k + kn)time polynomialspace algorithm for VERTEX COVER improving both the previous O(1.286 k +kn)time polynomialspace algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 k k 4 + kn)time exponentialspace algorithm, by Chandran and Grandoni. M ..."
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Abstract — This paper presents an O(1.2738 k + kn)time polynomialspace algorithm for VERTEX COVER improving both the previous O(1.286 k +kn)time polynomialspace algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 k k 4 + kn)time exponentialspace algorithm, by Chandran and Grandoni. Most of the previous algorithms rely on exhaustive casebycase analysis, and an underlying conservative worstcasescenario assumption. The contribution of the paper lies in the extreme simplicity, uniformity, and obliviousness of the algorithm presented. Several new techniques, as well as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis. The algorithm also induces improvement on the upper bound for the INDEPENDENT SET problem on graphs of degree bounded by 6. I.
Combinatorial genetic regulatory network analysis tools for high throughput transcriptomic data
 Proceedings, RECOMB Satellite Workshop on Systems Biology and Regulatory Genomics
, 2005
"... Abstract: A series of genomescale algorithms and highperformance implementations is described and shown to be useful in the genetic analysis of gene transcription. With them it is possible to address common questions such as: “are the sets of genes coexpressed under one type of conditions the same ..."
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Abstract: A series of genomescale algorithms and highperformance implementations is described and shown to be useful in the genetic analysis of gene transcription. With them it is possible to address common questions such as: “are the sets of genes coexpressed under one type of conditions the same as those sets coexpressed under another?” A new noiseadaptive graph algorithm, dubbed “paraclique, ” is introduced and analyzed for use in biological hypotheses testing. A notion of vertex coverage is also devised, based on vertexdisjoint paths within correlation graphs, and used to determine the identity, proportion and number of transcripts connected to individual phenotypes and quantitative trait loci (QTL) regulatory models. A major goal is to identify which, among a set of candidate genes, are the most likely regulators of trait variation. These methods are applied in an effort to identify multipleQTL regulatory models for large groups of genetically coexpressed genes, and to extrapolate the consequences of this genetic variation on phenotypes observed across levels of biological scale through the evaluation of vertex coverage. This approach is furthermore applied to definitions of homologybased gene sets, and the incorporation of categorical data such as known gene pathways. In all these tasks discrete mathematics and combinatorial algorithms form organizing principles upon which methods and implementations are based.
Exact algorithms and applications for Treelike Weighted Set Cover
 JOURNAL OF DISCRETE ALGORITHMS
, 2006
"... We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given ..."
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We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “treelike.” That is, the subsets in C can be organized in a tree T such that every subset onetoone corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edgeweighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = S, and m: = C. The algorithm also implies a fixedparameter tractability result for the NPcomplete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.