8- https://doi.org/10.1007/s00453-012-9694-7
Scheduling Partially Ordered Jobs Faster than 2 n
- Oct 9, 2012
- Algorithmica
- Marek Cygan +3 more
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 2n 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.
- # Total Completion Time
- # Precedence Constraints
- # Scheduling Problem
- # Processing Times
- # Total Time
- # Traveling Repairman Problem
- # Repairman Problem
- # Dynamic Programming Algorithm
- # Completion Time
- # Dynamic Programming
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