# A polynomial algorithm for $P | p_j = 1, r_j, outtree | \Sigma C_j$ and $P | p_j = 1,r_j, outtree, pmtn | \Sigma C_j$

Peter Brucker, Johann L. Hurink, Sigrid Knust

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### Abstract

A polynomial algorithm is proposed for two scheduling problems for which the complexity status was open. A set of jobs with unit processing times, release dates and outtree precedence relations has to be processed on parallel identical machines such that the total completion time $\sum C_j$ is minimized. It is shown that the problem can be solved in $O(n^2)$ time if no preemption is allowed. Furthermore, it is proved that allowing preemption does not reduce the optimal objective value, which verifies a conjecture of Baptiste and Timkovsky.
Original language English Enschede University of Twente, Faculty of Mathematical Sciences Published - 2001

### Publication series

Name Memorandum / Department of Applied Mathematics University of Twente, Faculty of Mathematical Sciences 1566 0169-2690

• MSC-90B35
• IR-65753
• EWI-3386

### Cite this

Brucker, P., Hurink, J. L., & Knust, S. (2001). A polynomial algorithm for $P | p_j = 1, r_j, outtree | \Sigma C_j$ and $P | p_j = 1,r_j, outtree, pmtn | \Sigma C_j$. (Memorandum / Department of Applied Mathematics; No. 1566). Enschede: University of Twente, Faculty of Mathematical Sciences.