Scheduling partially ordered jobs faster than 2n

Authors:
Marek Cygan;Marcin Pilipczuk;Michał Pilipczuk;Jakub Onufry Wojtaszczyk
Affiliations:
Institute of Informatics, University of Warsaw, Poland;Institute of Informatics, University of Warsaw, Poland;Institute of Informatics, University of Warsaw, Poland;Google Inc., Cracow, Poland
Venue:
ESA'11 Proceedings of the 19th European conference on Algorithms
Year:
2011

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Abstract

In the SCHED problem 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. SCHED is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2nnO(1) time, and whether there exists an algorithms solving SCHED in O(cn) time for some constant c