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14,956
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
Approximation Schemes
"... F14.4> ffl)OPT, where OPT denotes the value of an optimal solution to the given problem instance. 3. The running time of the algorithm is polynomial in the length of the (original) input and in 1=ffl. Definition 1.2 A polynomial time approximation scheme (PTAS) (for a given optimization problem ..."
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F14.4> ffl)OPT, where OPT denotes the value of an optimal solution to the given problem instance. 3. The running time of the algorithm is polynomial in the length of the (original) input and in 1=ffl. Definition 1.2 A polynomial time approximation scheme (PTAS) (for a given optimization
Approximation Schemes for . . .
, 2011
"... In correlation clustering, given similarity or dissimilarity information for all pairs of data items, the goal is to find a clustering of the items into similarity classes, with the fewest inconsistencies with the input. This problem is hard to approximate in general but we give arbitrarily good app ..."
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In correlation clustering, given similarity or dissimilarity information for all pairs of data items, the goal is to find a clustering of the items into similarity classes, with the fewest inconsistencies with the input. This problem is hard to approximate in general but we give arbitrarily good
Approximation Schemes  A Tutorial
, 2007
"... This tutorial provides an introduction into the area of polynomial time approximation schemes. The underlying ideas, the main tools, and the standard approaches for the construction of such schemes are explained ingreat detail and illustrated in many examples and exercises. The tutorial also discus ..."
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Cited by 13 (0 self)
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This tutorial provides an introduction into the area of polynomial time approximation schemes. The underlying ideas, the main tools, and the standard approaches for the construction of such schemes are explained ingreat detail and illustrated in many examples and exercises. The tutorial also
Approximation schemes for covering and packing problems in image processing and VLSI
 J. ACM
, 1985
"... A unified and powerful approach is presented for devising polynomial approximation schemes for many strongly NPcomplete problems. Such schemes consist of families of approximation algorithms for each desired performance bound on the relative error c> 0, with running time that is polynomial whe ..."
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Cited by 249 (0 self)
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A unified and powerful approach is presented for devising polynomial approximation schemes for many strongly NPcomplete problems. Such schemes consist of families of approximation algorithms for each desired performance bound on the relative error c> 0, with running time that is polynomial
An Approximation Scheme for Planar Graph TSP
, 1995
"... We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortestpath metric of a planar unweighted graph. We present a polynomialtime approximation scheme (PTAS) for this problem. ..."
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Cited by 53 (7 self)
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We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortestpath metric of a planar unweighted graph. We present a polynomialtime approximation scheme (PTAS) for this problem.
Approximation Schemes for Multidimensional Packing
, 2003
"... We consider a classic multidimensional generalization of the bin packing problem, namely, packing ddimensional rectangles into the minimum number of unit cubes. Our two results are: an asymptotic polynomial time approximation scheme for packing d dimensional cubes into the minimum number of unit c ..."
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We consider a classic multidimensional generalization of the bin packing problem, namely, packing ddimensional rectangles into the minimum number of unit cubes. Our two results are: an asymptotic polynomial time approximation scheme for packing d dimensional cubes into the minimum number of unit
Approximation schemes for strip packing
"... Abstract. We study two variants of the classical strip packing problem, or packing rectangles into a rectangle of fixed width and minimum height, a classical NPhard cutting stock problem. The first result presented in this paper is an OP T + O(1/ɛ 2) approximation scheme for resource augmented stri ..."
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Abstract. We study two variants of the classical strip packing problem, or packing rectangles into a rectangle of fixed width and minimum height, a classical NPhard cutting stock problem. The first result presented in this paper is an OP T + O(1/ɛ 2) approximation scheme for resource augmented
Optimization Problems with Approximation Schemes
 Annual Conference for Computer Science Logic, CSL’96, Springer LNCS 1258
, 1997
"... . In this paper we extend recent work about the relationship between the syntactic description of NP optimization problems and their approximation properties. In contrast to Max SNP we consider problems that take arbitrary weighted structures as input instances and we use the framework of Metafinite ..."
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Cited by 1 (0 self)
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of Metafinite Model Theory [5] to get a more general definability theory of optimization problems. We define a class Max \Phi and show that every problem in this class has a fully polynomialtime approximation scheme (FPTAS), i.e., can be approximated to every desired accuracy " in time polynomial
Results 1  10
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14,956