Search results for: JOB SCHEDULING UNIFORM MACHINES MAKESPAN TOTAL COMPLETION TIME APPROXIMATION SCHEME NP-HARDNESS INCOMPATIBILITY GRAPH - Bridge of Knowledge

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Search results for: JOB SCHEDULING UNIFORM MACHINES MAKESPAN TOTAL COMPLETION TIME APPROXIMATION SCHEME NP-HARDNESS INCOMPATIBILITY GRAPH

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Search results for: JOB SCHEDULING UNIFORM MACHINES MAKESPAN TOTAL COMPLETION TIME APPROXIMATION SCHEME NP-HARDNESS INCOMPATIBILITY GRAPH

  • Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines: Complexity and Algorithms

    Publication

    - ARTIFICIAL INTELLIGENCE - Year 2022

    In this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality:...

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  • Scheduling on Uniform and Unrelated Machines with Bipartite Incompatibility Graphs

    Publication

    - Year 2022

    The problem of scheduling jobs on parallel machines under an incompatibility relation is considered in this paper. In this model, a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same machine. We consider job scheduling under the incompatibility relation modeled by a bipartite graph, under the makespan optimality criterion, on uniform and unrelated machines. Unrelated machines...

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  • Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

    Publication

    In this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. Our research stems from the works of Bodlaender, Jansen, and Woeginger (1994) and Bodlaender and Jansen (1993). In particular, we pursue the...

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  • Total Completion Time Minimization for Scheduling with Incompatibility Cliques

    Publication

    - Year 2021

    This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent...

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  • Scheduling of identical jobs with bipartite incompatibility graphs on uniform machines. Computational experiments

    We consider the problem of scheduling unit-length jobs on three or four uniform parallel machines to minimize the schedule length or total completion time. We assume that the jobs are subject to some types of mutual exclusion constraints, modeled by a bipartite graph of a bounded degree. The edges of the graph correspond to the pairs of jobs that cannot be processed on the same machine. Although the problem is generally NP-hard,...

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