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13,461
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
The Foundation of Fixed Parameter Inapproximability
, 2013
"... Given an instance I of a minimization problem with optimum opt, fixed parameter ρ(k) inapproximability is to find a k ≥ opt and prove that it is not possible to compute a solution of value ρ(k) · k usually under the eth. In this paper we are interested only in k being the optimum value of some inst ..."
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Given an instance I of a minimization problem with optimum opt, fixed parameter ρ(k) inapproximability is to find a k ≥ opt and prove that it is not possible to compute a solution of value ρ(k) · k usually under the eth. In this paper we are interested only in k being the optimum value of some
FixedParameter Algorithms In Phylogenetics
, 2007
"... We survey the use of fixedparameter algorithms in the field of phylogenetics, which is the study of evolutionary relationships. The central problem in phylogenetics is the reconstruction of the evolutionary history of biological species, but its methods also apply to linguistics, philology or archi ..."
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Cited by 11 (1 self)
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We survey the use of fixedparameter algorithms in the field of phylogenetics, which is the study of evolutionary relationships. The central problem in phylogenetics is the reconstruction of the evolutionary history of biological species, but its methods also apply to linguistics, philology
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.
FixedParameter Complexity and Cryptography
, 1993
"... . We discuss the issue of the parameterized computational complexity of a number of problems of interest in cryptography. We show that the problem of determining whether an ndigit number has a prime divisor less than or equal to n k can be solved in expected time f(k)n 3 by a randomized algo ..."
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Cited by 20 (11 self)
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about implementations which fix a parameter such as the size or Hamming weight of keys. We show that several parameterized problems of relevance to cryptography, including kSubset Sum, kPerfect Code, and kSubset Product are likely to be intractable with respect to fixedparameter complexity
Distortion is Fixed Parameter Tractable
"... We study lowdistortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective. Let M = M(G) be the shortest path metric of an edge weighted graph G, with the vertex set V (G) and the edge set E(G), on n v ..."
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Cited by 3 (2 self)
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vertices. We give the first fixed parameter tractable algorithm that for an unweighted graph metric M and integer d either constructs an embedding of M into the line with distortion at most d, or concludes that no such embedding exists. Our algorithm requires O(nd 4 (2d + 1) 2d) time which is a significant
Imbalance is Fixed Parameter Tractable
"... Abstract. In the Imbalance Minimization problem we are given a graph G = (V, E) and an integer b and asked whether there is an ordering v1... vn of V such that the sum of the imbalance of all the vertices is at most b. The imbalance of a vertex vi is the absolute value of the difference between the ..."
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Cited by 1 (1 self)
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the number of neighbors to the left and right of vi. The problem is also known as the Balanced Vertex Ordering problem and it finds many applications in graph drawing. We show that this problem is fixed parameter tractable and provide an algorithm that runs in time 2 O(b log b) · n O(1). This resolves
On efficient fixedparameter algorithms for . . .
, 2000
"... We investigate the fixedparameter complexity of Weighted Vertex Cover. Given a graph G = (V, E), a weight function ω: V → R +, and k ∈ R +, Weighted Vertex Cover (WVC for short) asks for a vertex subset C ⊆ V of total weight at most k such that every edge of G has at least one endpoint in C. WVC an ..."
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We investigate the fixedparameter complexity of Weighted Vertex Cover. Given a graph G = (V, E), a weight function ω: V → R +, and k ∈ R +, Weighted Vertex Cover (WVC for short) asks for a vertex subset C ⊆ V of total weight at most k such that every edge of G has at least one endpoint in C. WVC
FixedParameter TRACTABILITY AND COMPLETENESS I: BASIC Results
, 1995
"... For many fixedparameter problems that are trivially soluable in polynomial time, such as (k)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as (k)FEEDBACK VERTEX SET, exhibit fixedparameter tractability: fo ..."
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Cited by 113 (16 self)
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For many fixedparameter problems that are trivially soluable in polynomial time, such as (k)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as (k)FEEDBACK VERTEX SET, exhibit fixedparameter tractability
Results 1  10
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13,461