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108,472
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 412 (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
Approximation by polynomials
, 1999
"... 2. The Weierstrass approximation theorem 3. Estimates for the Bernstein polynomials 4. Weierstrass ’ original proof ..."
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2. The Weierstrass approximation theorem 3. Estimates for the Bernstein polynomials 4. Weierstrass ’ original proof
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
Sequential and parallel complexity of approximate evaluation of polynomial zeros
 COMPUT. MATH. APPLIC
, 1987
"... Our new sequential and parallel algorithms establish new record upper bounds on both arithmetic and Boolean complexity of approximating to complex polynomial zeros. O(n 2 log b log n) arithmetic operations or O(n log n log (bn)) parallel steps and n log b/log (bn) processors suffice in order to appr ..."
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Cited by 20 (7 self)
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Our new sequential and parallel algorithms establish new record upper bounds on both arithmetic and Boolean complexity of approximating to complex polynomial zeros. O(n 2 log b log n) arithmetic operations or O(n log n log (bn)) parallel steps and n log b/log (bn) processors suffice in order
Results 1  10
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108,472