Paper Info
Title
On‐line approximation algorithms for scheduling tasks on identical machines withextendable working time
Abstract
We study the on-line problem of assigning tasks to identical machines whose regularworking time - assumed to be unitary - can be extended. If the tasks assigned to a machinedo not exceed the regular working time, then the working time of the machine is consideredto be 1; otherwise, it is the completion time of the last task assigned to the machine. Eachincoming task has to be assigned immediately to a machine and the assignment cannot bechanged later. The objective is to minimize the sum of the working times of the machines.Since the regular working time of the machines can be seen as a given capacity, the problemcan also be described through the bin packing terminology: the machines are viewed as binsand the tasks as items. A lower bound of 7/6 on the worst-case relative error of any on-linealgorithm is shown. Then it is shown that a list scheduling heuristic which assigns theincoming task to the machine with smallest current load has worst-case error equal to 5/4.The bound is improved to 1.228 by a new algorithm which tends to load the partially loadedmachines, as long as this does not cause an increase of the working time by more than afixed and appropriately chosen quantity x > 0.
Year
DOI
Venue
1999
10.1023/A:1018935608981
Annals OR
Keywords
DocType
Volume
bin packing,worst-case performance,on- line algorithms,scheduling on identical machines,extendable working time
Journal
86
Issue
ISSN
Citations 
0
1572-9338
4
PageRank 
References 
Authors
0.77
5
2
Name
Order
Citations
PageRank
M. G. Speranza129419.55
Zs Tuza236764.48