Weighted completion time minimization on a single-machine with a fixed non-availability interval: differential approximability

Imed Kacem (1, 2) , Vangelis Paschos (3)

1 LCOMS - Laboratoire de Conception, Optimisation et Modélisation des Systèmes
2 LITA - Laboratoire d'Informatique Théorique et Appliquée
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

This paper is the first successful attempt on differential approximability study for a scheduling problem. Such a study considers the weighted completion time minimization on a single machine with a fixed non-availability interval. The analysis shows that the Weighted Shortest Processing Time (WSPT) rule cannot yield a differential approximation for the studied problem in the general case. Nevertheless, a slight modification of this rule provides an approximation with a differential ratio of 3√5/2≈0.38.

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

Imed Kacem, Vangelis Paschos. Weighted completion time minimization on a single-machine with a fixed non-availability interval: differential approximability. 2011. ⟨hal-00875644⟩