Integer knapsacks: average behavior of the Frobenius numbers

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 and Henk, Martin 2009. Integer knapsacks: average behavior of the Frobenius numbers. Mathematics of Operations Research 34 (3) , pp. 698-705. 10.1287/moor.1090.0393

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Abstract

The largest integer that cannot be represented as a nonnegative integral combination of given set of positive integers is called the Frobenius number of these integers. We show that the asymptotic growth of the Frobenius number on average is significantly slower than the growth of the maximum Frobenius number.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	knapsack problem; Frobenius number; successive minima; inhomogeneous minimum; distribution of lattices
Publisher:	INFORMS
ISSN:	0364-765X
Last Modified:	13 Jan 2023 02:14
URI:	https://orca.cardiff.ac.uk/id/eprint/24991

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