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COMPLEXITY AND APPROXIMABILITY OF THE COVER POLYNOMIAL
"... Abstract. The cover polynomial and its geometric version introduced by Chung & Graham and D’Antona & Munarini, respectively, are twovariate graph polynomials for directed graphs. They count the (weighted) number of ways to cover a graph with disjoint directed cycles and paths, they can be t ..."
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Cited by 1 (0 self)
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the complexity of approximately evaluating the geometric cover polynomial. Under the reasonable complexity assumptions RP = NP and RFP = #P, we give a succinct characterization of a large class of points at which approximating the geometric cover polynomial within any polynomial factor is not possible.
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization
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
The communication complexity of approximate set packing and covering
 In ICALP 2002
, 2002
"... n))approximation for the packing number can be done with polynomial (in n) amount of communication, getting a (1=2 \Gamma ffl) log n approximation for the cover number or a better than min(k; n 1=2\Gamma ffl)approximation for the packing number requires exponential communication complexity. 1 Intr ..."
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Cited by 32 (11 self)
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n))approximation for the packing number can be done with polynomial (in n) amount of communication, getting a (1=2 \Gamma ffl) log n approximation for the cover number or a better than min(k; n 1=2\Gamma ffl)approximation for the packing number requires exponential communication complexity. 1
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
The complexity of the covering radius problem
 Computational Complexity
, 2005
"... Abstract. We initiate the study of the computational complexity of the covering radius problem for lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its re ..."
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Cited by 14 (4 self)
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Abstract. We initiate the study of the computational complexity of the covering radius problem for lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its
Polynomial RootFinding Algorithms and Branched Covers
 SIAM Journal of Computing
, 1994
"... Abstract. We construct a family of rootfinding algorithms which combine knowledge of the branched covering structure of a polynomial with a pathlifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an ǫfactorization of a polynomial of degree ..."
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Cited by 10 (1 self)
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of degree d which has an arithmetic complexity of O ( d(log d) 2  log ǫ  + d 2 (log d) 2). At the present time, this complexity is the best known in terms of the degree. Key words. Newton’s method, approximate zeros, arithmetic complexity, pathlifting method, branched covering. AMS subject
Exponentialtime approximation of weighted set cover
 Inf. Process. Lett
"... The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponentialtime algorithms for ..."
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Cited by 9 (0 self)
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The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponentialtime algorithms
Rectangle Size Bounds and Threshold Covers in Communication Complexity
 In Proceedings Eighteenth Annual IEEE Conference on Computational Complexity
, 2003
"... We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on the inputs. While it is known that the 0error version of th ..."
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Cited by 29 (5 self)
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relaxations of this notion, namely approximate majority covers and majority covers, and compare these three notions in power, exhibiting exponential separations. Each of these covers captures a lower bound method previously used for randomized communication complexity.
Results 1  10
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