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The planar directed kvertexdisjoint paths problem is fixedparameter tractable
 CORR
"... Given a graph G and k pairs of vertices (s1, t1),..., (sk, tk), the kVertexDisjoint Paths problem asks for pairwise vertexdisjoint paths P1,..., Pk such that Pi goes from si to ti. Schrijver [SICOMP’94] proved that the kVertexDisjoint Paths problem on planar directed graphs can be solved in ti ..."
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Given a graph G and k pairs of vertices (s1, t1),..., (sk, tk), the kVertexDisjoint Paths problem asks for pairwise vertexdisjoint paths P1,..., Pk such that Pi goes from si to ti. Schrijver [SICOMP’94] proved that the kVertexDisjoint Paths problem on planar directed graphs can be solved
Fixedparameter tractability and completeness
, 1992
"... For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDominating Set, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as kFeedback Vertex Set, exhibit fixedparameter tractability: for eac ..."
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Cited by 53 (6 self)
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For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDominating Set, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as kFeedback Vertex Set, exhibit fixedparameter tractability
Fixedparameter
"... tractable canonization and isomorphism test for graphs of bounded treewidth∗ ..."
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tractable canonization and isomorphism test for graphs of bounded treewidth∗
Fixedparameter
"... tractable canonization and isomorphism test for graphs of bounded treewidth∗ ..."
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tractable canonization and isomorphism test for graphs of bounded treewidth∗
Minimizing Movement: FixedParameter Tractability
"... Abstract. We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network m ..."
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Cited by 6 (2 self)
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inapproximability. Given that the number of mobile agents is typically much smaller than the complexity of the environment, we turn to fixedparameter tractability. We characterize the boundary between tractable and intractable movement problems in a very general set up: it turns out the complexity of the problem
Fixedparameter tractability and logic
 In preparation
, 1999
"... We exhibit a close connection between parameterized complexity theory and logic. Our approach is that of descriptive complexity theory. We study the definability of parameterized problems and try to obtain information about the parameterized complexity of the problems through the syntactical structu ..."
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Cited by 3 (2 self)
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structure of the defining sentences. On the one hand, we use this approach to prove that certain problems are fixedparameter tractable because they can be defined by syntactically simple formulas. On the other hand, we characterize classes of intractable problems by syntactical means. 1
DIRECTED GRAPHS: FIXEDPARAMETER TRACTABILITY & BEYOND
, 2014
"... Most interesting optimization problems on graphs are NPhard, implying that (unless P = NP) there is no polynomial time algorithm that solves all the instances of an NPhard problem exactly. However, classical complexity measures the running time as a function of only the overall input size. The pa ..."
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plexity is to design efficient algorithms for NPhard problems when the parameter k is small, even if the input size is large. Formally, we say that a parameterized problem is fixedparameter tractable (FPT) if instances of size n and parameter k can be solved in f (k) · nO(1) time, where f is a computable function
Subexponential fixedparameter tractability of cluster editing
, 2011
"... 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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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
Results 1  10
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214,299