On-line Bicriteria Interval Scheduling

Fabien Baille (1) , Evripidis Bampis (1) , Christian Laforest (1) , Nicolas Thibault (1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

We consider the problem of scheduling a sequence of intervals revealed on-line one by one in the order of their release dates on a set of k identical machines. Each interval i is associated with a processing time p i and a pair of arbitrary weights ( w i A, w i B) and may be scheduled on one of the k identical machines or rejected. The objective is to determine a valid schedule maximizing the sum of the weights of the scheduled intervals for each coordinate. We first propose a generic on-line algorithm based on the combination of two monocriteria on-line algorithms and we prove that it gives rise to a pair of competitive ratios that are function of the competitive ratios of the monocriteria algorithms in the input. We apply this technique to the special case where w i A=1 and w i B= p i for every interval and as a corollary we obtain a pair of constant competitive ratios.

Domains: Computer science; Operations Research [math.OC]; Data Structures and Algorithms [cs.DS]; Discrete Mathematics [cs.DM]; Computer Science and Game Theory [cs.GT]

Fabien Baille, Evripidis Bampis, Christian Laforest, Nicolas Thibault. On-line Bicriteria Interval Scheduling. Euro-Par 2005, 2005, Portugal. pp.312--322, ⟨10.1007/11549468_36⟩. ⟨hal-00341367⟩