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A New Fully Polynomial Approximation Scheme for the Knapsack Problem
 Proceedings 1st International Workshop on Approximation Algorithms for Combinatorial Optimization
, 1998
"... A new fully polynomial approximation scheme (FPTAS) is presented for the classical 01 knapsack problem. It considerably improves the space requirements. The two best previously known approaches need O(n+1=" 3 ) and O(n \Delta 1=") space, respectively. Our new approximation scheme requ ..."
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Cited by 16 (1 self)
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A new fully polynomial approximation scheme (FPTAS) is presented for the classical 01 knapsack problem. It considerably improves the space requirements. The two best previously known approaches need O(n+1=" 3 ) and O(n \Delta 1=") space, respectively. Our new approximation scheme
Polynomial Approximation Schemes for Smoothed and Random Instances of Multidimensional Packing Problems
"... Abstract The multidimensional bin packing and vector bin packingproblems are known to not have asymptotic polynomialtime approximation schemes (unless P = NP). Nevertheless, weshow that: * Any smoothed (randomly perturbed) instance, and anyinstance from a class of other distributions, does have a p ..."
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Cited by 5 (0 self)
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Abstract The multidimensional bin packing and vector bin packingproblems are known to not have asymptotic polynomialtime approximation schemes (unless P = NP). Nevertheless, weshow that: * Any smoothed (randomly perturbed) instance, and anyinstance from a class of other distributions, does have a
A POLYNOMIAL APPROXIMATION SCHEME FOR SCHEDULING ON UNIFORM PROCESSORS: USING THE DUAL APPROXIMATION APPROACH*
, 1988
"... Abstract. We present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as qu ..."
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Abstract. We present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed
Fully Polynomial Approximation Schemes for SingleItem Capacitated Economic LotSizing Problems
, 1997
"... NP#hard cases of the single#item capacitated lot#sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until ..."
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Cited by 17 (1 self)
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, until now no polynomial approximation method is known which produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist, by presenting an even stronger result: the existence of fully polynomial approximation schemes
Fully Polynomial Approximation Schemes For a SingleItem Capacitated LotSizing with Lost Sales Problem
"... The singleitem capacitated lotsizing problem with setup and shortage costs is a production planning problem in which there is a timevarying demand over T periods. The production should satisfy a restricted capacity ct to meet the demand dt at each period t. Moreover, for each period t, an invento ..."
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The singleitem capacitated lotsizing problem with setup and shortage costs is a production planning problem in which there is a timevarying demand over T periods. The production should satisfy a restricted capacity ct to meet the demand dt at each period t. Moreover, for each period t, an inventory cost ht is attached to the item as
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
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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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 1010 (2 self)
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Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution
Results 1  10
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25,877