How to Pack Your Items When You Have to Buy Your Knapsack

Antonios Antoniadis*, Chien-Chung Huang, Sebastian Ott, José Verschae

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)

Abstract

In this paper we consider a generalization of the classical knapsack problem. While in the standard setting a fixed capacity may not be exceeded by the weight of the chosen items, we replace this hard constraint by a weight-dependent cost function. The objective is to maximize the total profit of the chosen items minus the cost induced by their total weight. We study two natural classes of cost functions, namely convex and concave functions. For the concave case, we show that the problem can be solved in polynomial time; for the convex case we present an FPTAS and a 2-approximation algorithm with the running time of O(n log n) , where n is the number of items. Before, only a 3-approximation algorithm was known.

We note that our problem with a convex cost function is a special case of maximizing a non-monotone, possibly negative submodular function.
Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2013
Subtitle of host publication38th International Symposium, MFCS 2013, Klosterneuburg, Austria, August 26-30, 2013. Proceedings
EditorsKrishnendu Chatterjee, Jirí Sgall
Place of PublicationBerlin, Heidelberg
PublisherSpringer
Pages62-73
ISBN (Electronic)978-3-642-40313-2
ISBN (Print)978-3-642-40312-5
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria
Duration: 26 Aug 201330 Aug 2013
Conference number: 38

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume8087
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013
Abbreviated titleMFCS
CountryAustria
CityKlosterneuburg
Period26/08/1330/08/13

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