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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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Cited by 27 (3 self)
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Abstract. Important generalizations of the Vertex Cover problem
Algorithms Column: The Vertex Cover Problem
"... In this column I give a slightly simpler proof of an old result by Nemhauser and Trotter [10]. It would be interesting to see for which other problems such results hold. One of the widely studied problems in Combinatorial Optimization is the Weighted Vertex Cover problem. Given a graph G = (V, E) wi ..."
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Cited by 5 (0 self)
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In this column I give a slightly simpler proof of an old result by Nemhauser and Trotter [10]. It would be interesting to see for which other problems such results hold. One of the widely studied problems in Combinatorial Optimization is the Weighted Vertex Cover problem. Given a graph G = (V, E
The minimum generalized vertex cover problem
 IN PROCEEDINGS OF THE 11TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS
, 2003
"... Let G = (V, E) be an undirected graph, with three numbers d0(e) ≥ d1(e) ≥ d2(e) ≥ 0 for each edge e ∈ E. A solution is a subset U ⊆ V and di(e) represents the cost contributed to the solution by the edge e if exactly i of its endpoints are in the solution. The cost of including a vertex v in the ..."
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Cited by 4 (1 self)
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in the solution is c(v). A solution has cost that is equal to the sum of the vertex costs and the edge costs. The minimum generalized vertex cover problem is to compute a minimum cost set of vertices. We study the complexity of the problem with the costs d0(e) = 1, d1(e) = α and d2(e) = 0 ∀e ∈ E and c(v) = β
On the MAX MIN VERTEX COVER problem
, 2013
"... We address the max min vertex cover problem, which is the maximization version of the well studied min independent dominating set problem, known to be NPhard and highly inapproximable in polynomial time. We present tight approximation results for this problem on general graphs, namely a polynomial ..."
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We address the max min vertex cover problem, which is the maximization version of the well studied min independent dominating set problem, known to be NPhard and highly inapproximable in polynomial time. We present tight approximation results for this problem on general graphs, namely a polynomial
On the MAX kVERTEX COVER problem
, 2011
"... Given a graph G(V,E) of order n and a constant k � n, the max kvertex cover problem consists of determining k vertices that cover the maximum number of edges in G. In its (standard) parameterized version, max kvertex cover can be stated as follows: “given G, k and parameter ℓ, does G contain k ver ..."
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Given a graph G(V,E) of order n and a constant k � n, the max kvertex cover problem consists of determining k vertices that cover the maximum number of edges in G. In its (standard) parameterized version, max kvertex cover can be stated as follows: “given G, k and parameter ℓ, does G contain k
Evolutionary Algorithms and the Vertex Cover Problem
, 2007
"... Experimental results have suggested that evolutionary algorithms may produce higher quality solutions for instances of Vertex Cover than a very well known approximation algorithm for this NPComplete problem. A theoretical analysis of the expected runtime of the (1+1)EA on a well studied instance ..."
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Cited by 15 (8 self)
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Experimental results have suggested that evolutionary algorithms may produce higher quality solutions for instances of Vertex Cover than a very well known approximation algorithm for this NPComplete problem. A theoretical analysis of the expected runtime of the (1+1)EA on a well studied instance
Complexity and approximation results for the connected vertex cover problem
"... We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APXhard in bipartite graphs and is 5/3approximable in any class of graphs wher ..."
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Cited by 11 (0 self)
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We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APXhard in bipartite graphs and is 5/3approximable in any class of graphs
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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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
Using DNA to Solve the Minimal Vertex Covering Problem
"... Abstract. Plasmid DNA algorithm of the minimal vertex covering problem is proposed upon the basic idea and operation of plasmid DNA computing model. In the plasmid DNA algorithm, though an appropriate encoding and the basic biological operation, we finish the generation and separation of solution. O ..."
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Abstract. Plasmid DNA algorithm of the minimal vertex covering problem is proposed upon the basic idea and operation of plasmid DNA computing model. In the plasmid DNA algorithm, though an appropriate encoding and the basic biological operation, we finish the generation and separation of solution
Test Sets for Vertex Cover Problems (Extended Abstract)
, 1999
"... We describe the structure of the unique minimal test set T for a family of vertex cover problems. The set T corresponds to the Gröbner basis of the binomial ideal for the problem as described in [1]. While T has a surprisingly simple structure, in particular when the underlying graph is complete, it ..."
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We describe the structure of the unique minimal test set T for a family of vertex cover problems. The set T corresponds to the Gröbner basis of the binomial ideal for the problem as described in [1]. While T has a surprisingly simple structure, in particular when the underlying graph is complete
Results 1  10
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2,005,159