, Volume 68, Issue 3, pp 692-714

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Scheduling Partially Ordered Jobs Faster than 2 n

  • Marek CyganAffiliated withInstitute of Informatics, University of Warsaw
  • , Marcin PilipczukAffiliated withInstitute of Informatics, University of Warsaw Email author 
  • , Michał PilipczukAffiliated withFaculty of Mathematics, Informatics and Mechanics, University of Warsaw
  • , Jakub Onufry WojtaszczykAffiliated withGoogle Inc.


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.


Moderately-exponential algorithms Dynamic programming 2 n -Barrier Scheduling Partially ordered jobs