Integer Knapsacks: Average Behavior of the Frobenius Numbers
Iskander Aliev, Martin Henk
TL;DR
This paper investigates the average growth rate of Frobenius numbers in integer knapsack problems, revealing it increases more slowly than the maximum Frobenius number, thus providing new insights into their asymptotic behavior.
Contribution
It establishes that the average Frobenius number grows asymptotically slower than the maximum, offering a novel understanding of their typical behavior.
Findings
Average Frobenius number grows slower than maximum
Asymptotic analysis of Frobenius numbers
New insights into integer knapsack problems
Abstract
The main result of the paper shows that the asymptotic growth of the Frobenius number in average is significantly slower than the growth of the maximum Frobenius number.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Complexity and Algorithms in Graphs · Commutative Algebra and Its Applications