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199
Fixedparameter tractability and data reduction for Multicut in Trees
 Networks
, 2005
"... We study an NPcomplete (and MaxSNPhard) communication problem on tree networks, the socalled Multicut in Trees: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. Multicut has been ..."
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Cited by 14 (4 self)
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been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomialtime approximation algorithms. By way of contrast, we provide a simple fixedparameter algorithm for Multicut in Trees showing
Fixedparameter tractability of multicut in directed acyclic graphs
, 2015
"... The Multicut problem, given a graph G, a set of terminal pairs T = {(si, ti)  1 ≤ i ≤ r}, and an integer p, asks whether one can find a cutset consisting of at most p nonterminal vertices that separates all the terminal pairs, i.e., after removing the cutset, ti is not reachable from si for each ..."
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Cited by 9 (0 self)
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1 ≤ i ≤ r. The fixedparameter tractability of Multicut in undirected graphs, parameterized by the size of the cutset only, has been recently proved by Marx and Razgon [SIAM J. Comput., 43 (2014), pp. 355–388] and, independently, by Bousquet, Daligault, and Thomassé [Proceedings of STOC, ACM, 2011
Subset feedback vertex set is fixedparameter tractable
, 2011
"... The classical FEEDBACK VERTEX SET problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fi ..."
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Cited by 9 (2 self)
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tractable was posed independently by Kawarabayashi and Saurabh in 2009. We answer this question affirmatively. We begin by showing that this problem is fixedparameter tractable when parametrized by S. Next we present an algorithm which reduces the given instance to 2 k n O(1) instances with the size
Fixedparameter tractability and improved approximations for segment minimization
, 2009
"... The segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one nonzero value, and the nonzeroes in each row are consecutive. This has direct applications in intensitymodulated radiation therapy, ..."
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Cited by 2 (1 self)
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, an effective form of cancer treatment. We show here that for the case of an 1 × nmatrix, this problem is fixedparameter tractable in the largest value of the intensity matrix. We use this to develop approximation algorithms for matrices with arbitrarily many rows. One of these improves the approximation
Subexponential fixedparameter tractability of cluster editing
, 2012
"... In the Correlation Clustering, also known as Cluster Editing, we are given an undirected nvertex graph G and a positive integer k. The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by changing at most k adjacencies, i.e. by adding/deleting at mo ..."
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Cited by 4 (0 self)
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/deleting at most k edges. We give a subexponential algorithm that • in time 2O( pk) + nO(1) decides whether G can be transformed into a cluster graph with p cliques by changing at most k adjacencies. We complement our algorithmic findings by the following tight lower bounds on the asymptotic behaviour of our
Practical algorithms and fixedparameter tractability for the single individual SNP haplotyping problem
 In Proceedings of the 2nd Inter national Workshop on Algorithms in Bioinformatics, (WABI
"... Abstract. Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation, of foremost importance for a variety of applications including medical diagnostic, phylogenies and drug design. The complete SNPs sequence information from each of the two copies of a given chromo ..."
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Cited by 27 (5 self)
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chromosome in a diploid genome is called a haplotype. The Haplotyping Problem for a single individual is as follows: Given a set of fragments from one individual’s DNA, find a maximally consistent pair of SNPs haplotypes (one per chromosome copy) by removing data “errors” related to sequencing errors
Faster fixedparameter tractable algorithms for matching and packing problems. In:
 Proceedings of the 12th Annual European Symposium on Algorithms (ESA),
, 2004
"... Abstract We obtain faster algorithms for problems such as rdimensional matching and rset packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). This technique lets us com ..."
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Cited by 22 (1 self)
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combine Alon, Yuster and Zwick's colorcoding technique with dynamic programming to obtain faster fixedparameter algo rithms for these problems. Our algorithms run in time O(n + 2 O(k) ), an improvement over previous algorithms for some of these problems running in time O(n + k O
FixedParameter Tractability Results for FullDegree Spanning Tree and Its Dual
 In Proc. the 2nd International Workshop on Parameterized and Exact Computation (IWPEC), Springer LNCS
, 2006
"... We provide firsttime fixedparameter tractability results for the NPhard problems Maximum FullDegree Spanning Tree and MinimumVertex Feedback Edge Set. These problems are dual to each other: In Maximum FullDegree Spanning Tree, the task is to find a spanning tree for a given graph that maximizes ..."
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Cited by 13 (2 self)
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We provide firsttime fixedparameter tractability results for the NPhard problems Maximum FullDegree Spanning Tree and MinimumVertex Feedback Edge Set. These problems are dual to each other: In Maximum FullDegree Spanning Tree, the task is to find a spanning tree for a given graph
Drawing (complete) binary tanglegrams: Hardness, approximation, fixedparameter tractability
, 2008
"... A binary tanglegram is a pair 〈S, T 〉 of binary trees whose leaf sets are in onetoone correspondence; matching leaves are connected by intertree edges. For applications, for example in phylogenetics, it is essential that both trees are drawn without edge crossings and that the intertree edges ..."
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Cited by 9 (2 self)
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have as few crossings as possible. It is known that finding a drawing with the minimum number of crossings is NPhard and that the problem is fixedparameter tractable with respect to that number. We prove that under the Unique Games Conjecture there is no constantfactor approximation for general
Results 1  10
of
199