NDLI: Gradient elements of the knapsack polytope

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Gradient elements of the knapsack polytope

Content Provider	Springer Nature Link
Author	Brimkov, V. E. Barneva, R. P.
Copyright Year	2001
Abstract	The knapsack problem is a classical NP-hard problem of special interest in combinatorial mathematics and complexity theory. Particularly interesting are the properties of the knapsack problem domain. In this paper we study the set of gradient elements of the knapsack polytope. They are related with the well-known greedy algorithm for finding approximate solutions to the optimization knapsack problem and constitute an important subset of the extremal elements (vertices) of the knapsack polytope. We obtain a tight bound for the number of distinct gradient elements, which is an exponential function of the problem dimension. We also use the greedy-algorithmic approach and the concept of gradient elements to devise a polynomial algorithm for a large subclass of a linear Diophantine problem which is a variant of the knapsack problem. Some optimization issues related to the problems considered are discussed as well.
Starting Page	49
Ending Page	66
Page Count	18
File Format	PDF
ISSN	00080624
Journal	CALCOLO
Volume Number	38
Issue Number	1
e-ISSN	11265434
Language	English
Publisher	Springer-Verlag
Publisher Date	2001-03-01
Publisher Place	Milano
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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