A Fixed-Parameter Algorithm for Scheduling Unit Dependent Tasks on Parallel Machines with Time Windows

Alix Munier Kordon (1)

1 ALSOC - Architecture et Logiciels pour Systèmes Embarqués sur Puce

This paper proves that the existence of a feasible schedule for a set of dependent tasks of unit execution times with release dates and deadlines on a limited number of processors is a fixed-parameter tractable problem. The parameter considered is the pathwidth of the interval graph associated with the time windows of the tasks. A fixed-parameter algorithm based on a dynamic programming approach is developed and proved to solve this decision problem. Fixed-parameter algorithms for the two classical problems P |prec, p i = 1, r i |C max and P |prec, p i = 1, r i |L max are then derived using a binary search. They are, as far as we know, the first fixed-parameter algorithms for these scheduling problems.

Mots clés: parallel identical machines; makespan; maximum lateness; parameterized complexity

Domaines: Algorithme et structure de données [cs.DS]; Recherche opérationnelle [math.OC]

Alix Munier Kordon. A Fixed-Parameter Algorithm for Scheduling Unit Dependent Tasks on Parallel Machines with Time Windows. Discrete Applied Mathematics, 2020. ⟨hal-03041735⟩