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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

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Better polynomial algorithms for scheduling unit-length jobswith bipartite incompatibility graphs on uniform machines

Pikies T., Kubale Marek

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 1

31--36

The goal of this paper is to explore and to provide tools for the investigation of the problems of unit-length scheduling of incompatible jobs on uniform machines. We present two new algorithms that are a significant improvement over the known algorithms. The first one is Algorithm 2 which is 2-approximate for the problem Qm|pj = 1, G = bisubquartic|Cmax. The second one is Algorithm 3 which is 4-approximate for the problem Qm|pj = 1, G = bisubquartic|ΣCj, where m ϵ {2, 3, 4}. The theory behind the proposed algorithms is based on the properties of 2-coloring with maximal coloring width, and on the properties of ideal machine, an abstract machine that we introduce in this paper.

Algorithms for parallel processor scheduling with distinct due windows and unit-time jobs

Janiak A., Janiak W.A., Januszkiewicz R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2009

Vol. 57, nr 3

209-215

We have studied problems of scheduling n unit-time jobs on m identical parallel processors, in which for each job a distinct due window is given in advance. If a job is completed within its due window, then it incurs no penalty. Otherwise, it incurs a job-dependent earliness or tardiness cost. The objective is to find a job schedule such that the total weighted earliness and tardiness, maximum weighted earliness and tardiness or total weighted number of early and lardy jobs is minimized. Properties of optimal solutions of these problems are established. We proved that optimal solutions for these problems can be found in O(n5) time in case of minimization of the total weighted earliness and tardiness and the total weighted number of early and tardy jobs and in O (n4 n log n) time in case of minimization of the maximum weighted earliness and tardiness. The established solution methods are extended to solve the problems with arbitrary integer release dates. A dedicated algorithm with time complexity O(n3) is provided for the special case of the problem of minimizing total weighted number of early and tardy jobs with agreeable earliness-tardiness weights.