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FixedParameter Evolutionary Algorithms and the Vertex Cover Problem
"... In this paper, we consider multiobjective evolutionary algorithms for the Vertex Cover problem in the context of parameterized complexity. We relate the runtime of our algorithms to the input size and the cost of a minimum solution and point out that the search process of evolutionary algorithms cr ..."
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Cited by 8 (4 self)
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.e. the expected runtime is bounded by O(f(OPT) · n c), where c is a constant and f a function that only depends on OPT. This shows that evolutionary algorithms are randomized fixedparameter tractable algorithms for the vertex cover problem.
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
, 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 algorithms for . . .
, 2003
"... FestparameterAlgorithmen bieten einen konstruktiven Ansatz zur Losung von kombinatorisch schwierigen, in der Regel NPharten Problemen, der zwei Ziele berucksichtigt: innerhalb von beweisbaren Laufzeitschranken werden optimale Ergebnisse berechnet. Die entscheidende Idee ist dabei, einen oder mehr ..."
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Cited by 1 (0 self)
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mehrere Aspekte der Problemeingabe als Parameter der Problems aufzufassen und die kombinatorische Explosion der algorithmischen Schwierigkeit auf diese Parameter zu beschranken, so dass die Laufzeitkosten polynomiell in Bezug auf den nichtparametrisierten Teil der Eingabe sind. Gibt es einen
FixedParameter Algorithms for . . .
 ROCEEDINGS OF THE 30TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP’03)
, 2003
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Two FixedParameter Algorithms for Vertex Covering by Paths on Trees 1
"... Vertex Covering by Paths on Trees with applications in machine translation is the task to cover all vertices of a tree T = (V,E) by choosing a minimumweight subset of given paths in the tree. The problem is NPhard and has recently been solved by an exact algorithm running in O(4 C · V  2) time, ..."
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Cited by 2 (0 self)
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on Trees, we present an exact algorithm using a search tree of size O(2 k · k!), where k denotes the number of chosen covering paths. Finally, we briefly discuss the existence of a sizeO(k 2) problem kernel. Key words: graph algorithms, combinatorial problems, fixedparameter tractability, exact
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Results 1  10
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1,316,505