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Vertex Cover Might be Hard to Approximate to within 2ɛ
 IN PROCEEDINGS OF THE 18TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 2003
"... We show that vertex cover is hard to approximate within any constant factor better than 2 where the hardness is based on a conjecture regarding the power of unique 2prover1round games presented in [15]. We actually show a stronger result, namely, based on the same conjecture, vertex cover on k ..."
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Cited by 119 (11 self)
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We show that vertex cover is hard to approximate within any constant factor better than 2 where the hardness is based on a conjecture regarding the power of unique 2prover1round games presented in [15]. We actually show a stronger result, namely, based on the same conjecture, vertex cover on kuniform hypergraphs is hard to approximate within any constant factor better than k.
The Importance of Being Biased
, 2002
"... The Minimum Vertex Cover problem is the problem of, given a graph, finding a smallest set of vertices that touches all edges. We show that it is NPhard to approximate this problem 1.36067, improving on the previously known hardness result for a 6 factor. 1 ..."
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Cited by 86 (8 self)
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The Minimum Vertex Cover problem is the problem of, given a graph, finding a smallest set of vertices that touches all edges. We show that it is NPhard to approximate this problem 1.36067, improving on the previously known hardness result for a 6 factor. 1
Approximations of Weighted Independent Set and Hereditary Subset Problems
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2000
"... The focus of this study is to clarify the approximability of weighted versions of the maximum independent set problem. In particular, we report improved performance ratios in boundeddegree graphs, inductive graphs, and general graphs, as well as for the unweighted problem in sparse graphs. Wher ..."
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Cited by 53 (6 self)
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The focus of this study is to clarify the approximability of weighted versions of the maximum independent set problem. In particular, we report improved performance ratios in boundeddegree graphs, inductive graphs, and general graphs, as well as for the unweighted problem in sparse graphs. Where possible, the techniques are applied to related hereditary subgraph and subset problem, obtaining ratios better than previously reported for e.g. Weighted Set Packing, Longest Common Subsequence, and Independent Set in hypergraphs.
A new multilayered PCP and the hardness of hypergraph vertex cover
 In Proceedings of the 35th Annual ACM Symposium on Theory of Computing
, 2003
"... Abstract Given a kuniform hypergraph, the EkVertexCover problem is to find the smallest subsetof vertices that intersects every hyperedge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that EkVertexCover is NPhard toapproximate within a ..."
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Cited by 53 (10 self)
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Abstract Given a kuniform hypergraph, the EkVertexCover problem is to find the smallest subsetof vertices that intersects every hyperedge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that EkVertexCover is NPhard toapproximate within a factor of ( k 1 ") for arbitrary constants "> 0 and k> = 3. The resultis nearly tight as this problem can be easily approximated within factor k. Our constructionmakes use of the biased LongCode and is analyzed using combinatorial properties of swise tintersecting families of subsets.We also give a different proof that shows an inapproximability factor of b k 2 c ". In additionto being simpler, this proof also works for superconstant values of k up to (log N)1/c where
Dependent rounding and its applications to approximation algorithms
 Journal of the ACM
, 2006
"... Abstract We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multi ..."
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Cited by 46 (5 self)
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Abstract We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multipath routing; ffl richer randomgraph models for graphs with a given degreesequence; ffl improved approximation algorithms for: (i) throughputmaximization in broadcast scheduling, (ii) delayminimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and
A better approximation ratio for the vertex cover problem
, 2005
"... We reduce the approximation factor for Vertex Cover to 2 − Θ ( 1 √ log n) (instead of the previous log log n 2 − Θ ( log n), obtained by BarYehuda and Even [2], and by Monien and Speckenmeyer [10]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, ..."
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Cited by 45 (0 self)
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We reduce the approximation factor for Vertex Cover to 2 − Θ ( 1 √ log n) (instead of the previous log log n 2 − Θ ( log n), obtained by BarYehuda and Even [2], and by Monien and Speckenmeyer [10]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, and Vazirani [1] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and wellseparated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven in [1]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big wellseparated sets in the sense of [1] translates into the existence of a big independent set. 1
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 19 (2 self)
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Abstract. Important generalizations of the Vertex Cover problem
Approximating Coloring and Maximum Independent Sets in 3Uniform Hypergraphs
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2001
"... We discuss approximation algorithms for the coloring problem and the maximum independent set problem in 3uniform hypergraphs. An algorithm for coloring 3uniform 2colorable hypergraphs in ~ O(n 1=5 ) colors is presented, improving previously known results. Also, for every xed > 1=2, we describe ..."
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Cited by 17 (1 self)
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We discuss approximation algorithms for the coloring problem and the maximum independent set problem in 3uniform hypergraphs. An algorithm for coloring 3uniform 2colorable hypergraphs in ~ O(n 1=5 ) colors is presented, improving previously known results. Also, for every xed > 1=2, we describe an algorithm that, given a 3uniform hypergraph H on n vertices with an independent set of size n, nds an independent set of size ~ 3196 n; n 6 3 )). For certain values of we are able to improve this using the Local Ratio Approach. The results are obtained through Semidenite Programming relaxations of these optimization problems. 1