New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks

Enrico Angelelli (1) , Maria Grazia Speranza (1) , Zsolt Tuza (2, 3)

1 Department of Quantitative Methods [Brescia]
2 MTA SZTAKI - Computer and Automation Research Institute [Budapest]
3 Department of Computer Science and Systems Technology [Veszprem]

In this paper we study a semi on-line version of the classical multiprocessor scheduling problem on two identical processors. We assume that the sum of the tasks and an upper bound gamma on the size of each task are known. Each task has to be assigned upon arrival and the assignment cannot be changed later. The objective is the minimization of the maximum completion time on the processors. In this paper we propose new algorithms and improve known lower and upper bounds on the competitive ratio. Algorithms and bounds depend on the value of gamma. An optimal algorithm is obtained for gamma in the interval [ 1/n,2(n+1)/n(2n+1) ] and gamma = (2n-1)/2n(n-1), where n is any integer value larger or equal 2.

Mots clés: semi on-line scheduling; parallel processors; competitive analysis

Domaines: Mathématique discrète [cs.DM]

Enrico Angelelli, Maria Grazia Speranza, Zsolt Tuza. New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks. Discrete Mathematics and Theoretical Computer Science, 2006, Vol. 8, pp.1-16. ⟨10.46298/dmtcs.367⟩. ⟨hal-00961099⟩