NDLI: First-Fit Algorithm for the On-Line Chain Partitioning Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bosek, Bartomiej Szczypka, Edward Krawczyk, Tomasz
Copyright Year	2010
Abstract	We consider a problem of partitioning a partially ordered set into chains by first-fit algorithm. In general this algorithm uses arbitrarily many chains on a class of bounded width posets. In this paper we prove that First-Fit uses at most $3tw^2$ chains to partition any poset of width w which does not induce two incomparable chains of height t. In this way we get a wide class of posets with polynomial bound for the on-line chain partitioning problem. We also discuss some consequences of our result for coloring graphs by First-Fit.
Starting Page	1992
Ending Page	1999
Page Count	8
File Format	PDF
ISSN	08954801
DOI	10.1137/090753863
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-01-06
Access Restriction	Subscribed
Subject Keyword	Factorization, matching, partitioning, covering and packing Partial order, general Combinatorics of partially ordered sets on-line Structural characterization of families of graphs chain partition poset Games on graphs Partitions of sets Coloring of graphs and hypergraphs first-fit
Content Type	Text
Resource Type	Article
Subject	Mathematics

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

First-Fit Algorithm for the On-Line Chain Partitioning Problem