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Preprints 2010

A Robust PTAS for Machine Covering and Packing
Citation key Report-011-2010
Author Martin Skutella and Jose Verschae
Year 2010
Number 011
Institution Technische Universität Berlin, Institut für Mathematik
Abstract Scheduling a set of n jobs on m identical parallel machines so as to minimize the makespan or maximize the minimum machine load are two of the most important and fundamental scheduling problems studied in the literature. We consider the general online scenario where jobs are consecutively added to and/or deleted from an instance. The goal is to always maintain a (close to) optimal assignment of the current set of jobs to the m machines. This goal is essentially doomed to failure unless, upon arrival or departure of a job, we allow to reassign some other jobs. Considering that the reassignment of a job induces a cost proportional to its size, the total cost for reassigning jobs must preferably be bounded by a constant times the total size of added or deleted jobs.
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