, Volume 68, Issue 3, pp 692-714,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 09 Oct 2012

Scheduling Partially Ordered Jobs Faster than 2 n

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.

An extended abstract of this paper appears at 19th European Symposium on Algorithms, Saarbrücken, Germany, 2011.
M. Cygan and Marcin Pilipczuk were supported by Polish Ministry of Science grant no. N206 355636 and Foundation for Polish Science.