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2,860
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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Cited by 1 (0 self)
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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
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 751 (11 self)
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for the efficient approximability of many optimization problems studied previously. In particular, for MaxE2Sat, MaxCut, MaxdiCut, and Vertex cover. Warning: Essentially this paper has been published in JACM and is subject to copyright restrictions. In particular it is for personal use only.
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
Improved Nonapproximability Results for Minimum Vertex Cover with Density Constraints
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY
, 1996
"... We provide new nonapproximability results for the restrictions of the Min Vertex Cover problem to boundeddegree, sparse and dense graphs. We show that for a sufficiently large B, the recent 16/15 lower bound proved by Bellare et al. [5] extends with negligible loss to graphs with bounded degree ..."
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Cited by 16 (0 self)
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We provide new nonapproximability results for the restrictions of the Min Vertex Cover problem to boundeddegree, sparse and dense graphs. We show that for a sufficiently large B, the recent 16/15 lower bound proved by Bellare et al. [5] extends with negligible loss to graphs with bounded degree
Hypercontractive inequalities via SOS, with an application to VertexCover
, 2012
"... Our main result is a formulation and proof of the reverse hypercontractive inequality in the sumofsquares (SOS) proof system. As a consequence, we show that for any constant γ> 0, the O(1/γ)round SOS/Lasserre SDP hierarchy certifies the statement “MinVertexCover(G n γ) ≥ (1 − on(1))V ”, wh ..."
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Cited by 1 (1 self)
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Our main result is a formulation and proof of the reverse hypercontractive inequality in the sumofsquares (SOS) proof system. As a consequence, we show that for any constant γ> 0, the O(1/γ)round SOS/Lasserre SDP hierarchy certifies the statement “MinVertexCover(G n γ) ≥ (1 − on(1))V
Improved Nonapproximability Results for Vertex Cover with Density Constraints
 Proc. 2nd Int. Conference, COCOON '96, SpringerVerlag
, 1996
"... . We provide new nonapproximability results for the restrictions of the Min Vertex Cover problem to boundeddegree, sparse and dense graphs. We show that, for a sufficiently large B, the recent 16/15 lower bound proved by Bellare et al. [3] extends with negligible loss to graphs with bounded degree ..."
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Cited by 14 (1 self)
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. We provide new nonapproximability results for the restrictions of the Min Vertex Cover problem to boundeddegree, sparse and dense graphs. We show that, for a sufficiently large B, the recent 16/15 lower bound proved by Bellare et al. [3] extends with negligible loss to graphs with bounded
Vertex Cover: Further Observations and Further Improvements
 Journal of Algorithms
, 1999
"... Recently, there have been increasing interests and progresses in lowering the worst case time complexity for wellknown NPhard problems, in particular for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated and several simple and new techniques are int ..."
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Cited by 186 (19 self)
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Recently, there have been increasing interests and progresses in lowering the worst case time complexity for wellknown NPhard problems, in particular for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated and several simple and new techniques
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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), is by Nemhauser and Trotter [10]. Consider the following simple Integer Program (IP) for the Weighted Vertex Cover Problem. Here Xu refers to a binary indicator variable, and its value is 1 if and only if vertex u is in the cover. subject to min ~ Wu • Xu u6V
Vertex Cover Might be Hard to Approximate to within 2  ɛ
"... Based on a conjecture regarding the power of unique 2prover1round games presented in [Khot02], we show that vertex cover is hard to approximate within any constant factor better than 2. We actually show a stronger result, namely, based on the same conjecture, vertex cover on kuniform hypergraph ..."
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Cited by 151 (11 self)
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Based on a conjecture regarding the power of unique 2prover1round games presented in [Khot02], we show that vertex cover is hard to approximate within any constant factor better than 2. We actually show a stronger result, namely, based on the same conjecture, vertex cover on k
Results 1  10
of
2,860