Lower bounds for online makespan minimization on a small number of related machines

Authors:
Łukasz Jeż;Jarett Schwartz;Jiří Sgall;József Békési
Affiliations:
Institute of Computer Science, University of Wrocław, Wrocław, Poland 50-383 and Institute of Mathematics, Academy of Sciences of the Czech Republic, Praha 1, Czech Republic 115 67;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 1, Czech Republic 11800;Faculty of Mathematics and Physics, Computer Science Inst. of Charles University, Praha 1, Czech Republic 11800;Department of Applied Informatics, Gyula Juhász Faculty of Education, University of Szeged, Szeged, Hungary 6701
Venue:
Journal of Scheduling
Year:
2013

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Abstract

In online makespan minimization, the jobs characterized by their processing time arrive one-by-one and each has to be assigned to one of the m uniformly related machines. The goal is to minimize the length of the schedule. We prove new combinatorial lower bounds for m=4 and m=5, and computer-assisted lower bounds for m≤11.