A fixed-parameter algorithm for a unit-execution-time unit-communication-time tasks scheduling problem with a limited number of identical processors

Alix Munier-Kordon (1) , Ning Tang (1)

1 ALSOC - Architecture et Logiciels pour Systèmes Embarqués sur Puce

This paper considers the minimization of the maximum lateness for a set of dependent tasks with unit duration, unit communication delays release times and due dates. The number of processors is limited, and each task requires one processor for its execution. A time window built from an upper bound of the minimum maximum lateness is associated to each task. The parameter considered is the pathwidth of the associated interval graph. A fixed-parameter algorithm based on a dynamic programming approach is developed to solve this optimization problem. This is, as far as we know, the first fixed-parameter algorithm for a scheduling problem with communication delays and a limited number of processors.

Mots clés: Scheduling; communication delays; minimization of the maximum lateness; fixed-parameter algorithm

Domaines: Mathématiques [math]

Alix Munier-Kordon, Ning Tang. A fixed-parameter algorithm for a unit-execution-time unit-communication-time tasks scheduling problem with a limited number of identical processors. RAIRO - Operations Research, 2022, 56 (5), pp.3777-3788. ⟨10.1051/ro/2022174⟩. ⟨hal-03836225⟩