Journal ArticleDOI
Approximation algorithms for the m-dimensional 0–1 knapsack problem: Worst-case and probabilistic analyses
Alan Frieze,M.R.B. Clarke +1 more
TLDR
A polynomial approximation scheme for an m-constraint 0–1 integer programming problem (m fixed) based on the use of the dual simplex algorithm for linear programming and the asymptotic properties of a particular random model are analyzed.About:
This article is published in European Journal of Operational Research.The article was published on 1984-01-01. It has received 187 citations till now. The article focuses on the topics: Polynomial-time approximation scheme & Change-making problem.read more
Citations
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Journal ArticleDOI
A Genetic Algorithm for the Multidimensional Knapsack Problem
P. C. Chu,John E. Beasley +1 more
TL;DR: A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach and is capable of obtaining high-quality solutions for problems of various characteristics.
Journal ArticleDOI
The multidimensional 0–1 knapsack problem: An overview
TL;DR: This paper surveys the main results of the multidimensional 0–1 knapsack problem and focuses on the theoretical properties as well as approximate or exact solutions of this special 0-1 program.
Journal ArticleDOI
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
Chandra Chekuri,Sanjeev Khanna +1 more
TL;DR: A polynomial time approximation scheme (PTAS) for MKP, which appears to be the strongest special case of GAP that is not APX-hard, and a PTAS-preserving reduction from an arbitrary instance of MKP to an instance with distinct sizes and profits.
Proceedings ArticleDOI
A PTAS for the multiple knapsack problem
Chandra Chekuri,Sanjeev Khanna +1 more
TL;DR: The main result of this paper is a polynomial time approximation scheme for MKP, which helps demarcate the boundary at which instances of GAP become APX-hard.
Journal ArticleDOI
Assortment Optimization Under Variants of the Nested Logit Model
TL;DR: This work studies a class of assortment optimization problems where customers choose among the offered products according to the nested logit model and develops parsimonious collections of candidate assortments with worst-case performance guarantees for NP-hard cases.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Approximation algorithms for combinatorial problems
TL;DR: For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.
Journal ArticleDOI
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Oscar H. Ibarra,Chul Kim +1 more
TL;DR: An algorithm is presented which finds for any 0 < e < 1 an approximate solution P satisfying (P* P)/P* < ~, where P* is the desired optimal sum.