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Polynomial Time Approximation Schemes
, 2005
"... Let Π be an NPhard optimization problem, and let A be an approximation algorithm for Π. For an instance I of Π, let A(I) denote the objective value when running A on I, and let OP T (I) denote the optimal objective value. The approximation ratio of A for the instance I is RA(I) = A(I)/OP T (I), th ..."
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Let Π be an NPhard optimization problem, and let A be an approximation algorithm for Π. For an instance I of Π, let A(I) denote the objective value when running A on I, and let OP T (I) denote the optimal objective value. The approximation ratio of A for the instance I is RA(I) = A(I)/OP T (I
On the efficiency of polynomial time approximation schemes
, 1997
"... A polynomial time approximation scheme (PTAS) for an optimization problem A is an algorithm that given in input an instance of A and E> 0 find;,; (1 + E)approximate solution in time that is polynomial for each fixed E. Typical running times are no(+) or 2” ’ n. While algorithms of the former kin ..."
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Cited by 37 (0 self)
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A polynomial time approximation scheme (PTAS) for an optimization problem A is an algorithm that given in input an instance of A and E> 0 find;,; (1 + E)approximate solution in time that is polynomial for each fixed E. Typical running times are no(+) or 2” ’ n. While algorithms of the former
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
 Journal of the ACM
, 1998
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes ..."
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Cited by 397 (2 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
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Cited by 102 (5 self)
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A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total
Polynomialtime Approximation Scheme for Euclidean TSP (Lecture)
, 2007
"... We present a surprising result that the traveling salesman problem has a polynomialtime approximation scheme when the distances between cities are Euclidean. This result, independently due to Arora and Mitchell [1, 6], hinges on a powerful technique for randomly decomposing the given ..."
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We present a surprising result that the traveling salesman problem has a polynomialtime approximation scheme when the distances between cities are Euclidean. This result, independently due to Arora and Mitchell [1, 6], hinges on a powerful technique for randomly decomposing the given
On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization
 STACS'98, LNCS 1373
, 1998
"... Abstract The size of Ordered Binary Decision Diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory. The decision variant of the variable ordering problem is known to be ¡£¢complete. We strengthen this result ..."
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Cited by 20 (3 self)
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by showing that there in no polynomial time approximation scheme for the variable ordering problem unless ¢¥¤¥¡£¢. We also prove a small lower bound on the performance ratio of a polynomial time approximation algorithm under the assumption ¢§ ¦ ¤¥¡£¢
The Measure Hypothesis and Efficiency of Polynomial Time Approximation Schemes
, 2008
"... A polyomial time approximation scheme for an optimization problem X is an algorithm A such that for each instance x of X and each ffl> 0, A computes a (1 + ffl)approximate solution to instance x of Xin time is O(xf(1/ffl)) for some function f. If the running time of A isinstead bounded by g(1 ..."
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(1/ffl) * xO(1) for some function g, A is called anefficient polynomial time approximation scheme.
PolynomialTime Approximation Scheme for Data Broadcast
 STOC
, 2000
"... The data broadcast problem is to find a schedule for broadcasting a given set of messages over multiple channels. The goal is to minimize the cost of the broadcast plus the expected response time to clients who periodically and probabilistically tune in to wait for particular messages. The problem ..."
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Cited by 39 (3 self)
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we present the first polynomialtime approximation scheme for the data broadcast problem for the case when W = O(1) and each message has arbitrary probability, unit length and bounded cost. The best previous polynomialtime approximation algorithm for this case has a performance ratio of 9/8 [6].
A Polynomial Time Approximation Scheme for Dense Min 2Sat
, 2001
"... It is proved that everywheredense Min 2SAT and everywheredense Min Eq both have polynomial time approximation schemes. ..."
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Cited by 5 (2 self)
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It is proved that everywheredense Min 2SAT and everywheredense Min Eq both have polynomial time approximation schemes.
Polynomial Time Approximation Schemes for Geometric kClustering
 J. OF THE ACM
, 2001
"... The JohnsonLindenstrauss lemma states that n points in a high dimensional Hilbert space can be embedded with small distortion of the distances into an O(log n) dimensional space by applying a random linear transformation. We show that similar (though weaker) properties hold for certain random linea ..."
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Cited by 40 (4 self)
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hard in some high dimensional geometric settings, even for k = 2. We give polynomial time approximation schemes for this problem in several settings, including the binary cube {0, 1}^d with Hamming distance, and R^d either with L¹ distance, or with L² distance, or with the square of L² distance
Results 1  10
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10,461