Cygan, Marek, Pilipczuk, Marcin, Pilipczuk, Michał and Wojtaszczyk, Jakub Onufry (2014) Scheduling partially ordered jobs faster than 2n. Algorithmica, Volume 68 (Number 3). pp. 692-714. doi:10.1007/s00453-012-9694-7 ISSN 0178-4617.

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Abstract

In a scheduling problem, denoted by 1|prec|∑C i in the Graham notation, we are given a set of n jobs, together with their processing times and precedence constraints. The task is to order the jobs so that their total completion time is minimized. 1|prec|∑C i is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2 n n O(1) time, and whether there exists an algorithms solving 1|prec|∑C i in O(c n ) time for some constant c<2 was an open problem posted in 2004 by Woeginger. In this paper we answer this question positively.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Dynamic programming, Computer scheduling
Journal or Publication Title:	Algorithmica
Publisher:	Springer
ISSN:	0178-4617
Official Date:	1 March 2014
Dates:	Date Event 1 March 2014 Published 9 October 2012 Available 24 September 2012 Accepted 20 December 2011 Submitted
Volume:	Volume 68
Number:	Number 3
Page Range:	pp. 692-714
DOI:	10.1007/s00453-012-9694-7
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	28 December 2015
Date of first compliant Open Access:	28 December 2015
Embodied As:	1

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