NDLI: Parameterized Approximation Scheme for the Multiple Knapsack Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Jansen, Klaus
Copyright Year	2009
Abstract	The multiple knapsack problem (MKP) is a well-known generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins (knapsacks) such that each item $a \in A$ has a size $size(a)$ and a profit value $profit(a)$, and each bin $b \in B$ has a capacity $c(b)$. The goal is to find a subset $U \subset A$ of maximum total profit such that U can be packed into B without exceeding the capacities. The decision version of MKP is strongly NP-complete, since it is a generalization of the classical knapsack and bin packing problem. Furthermore, MKP does not admit a fully time polynomial time approximation scheme (FPTAS) even if the number m of bins is two. Kellerer gave a polynomial time approximation scheme (PTAS) for MKP with identical capacities and Chekuri and Khanna presented a PTAS for MKP with general capacities with running time $n^{O(\log(1/\epsilon)/\epsilon^8)}$. In this paper we propose an efficient PTAS (EPTAS) with parameterized running time $2^{O(\log(1/\epsilon)/\epsilon^5)} \cdot poly(n) + O(m)$ for MKP. This also solves an open question by Chekuri and Khanna.
Starting Page	1392
Ending Page	1412
Page Count	21
File Format	PDF
ISSN	00975397
DOI	10.1137/080731207
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-10-16
Access Restriction	Subscribed
Subject Keyword	knapsack problem parameterized complexity Approximation algorithms Linear programming approximation algorithms Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in