A best possible online algorithm for scheduling equal-length jobs on two machines with chain precedence constraints

Authors:
Junling Yuan;Wenhua Li;Jinjiang Yuan
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China and School of Computer and Communication Engineering, University of Science and Technology Beiji ...;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We consider the online scheduling on two identical parallel machines with chain precedence constraints to minimize makespan, where jobs arrive over time and have identical processing times. For this online scheduling problem, Huo and Leung [Y. Huo and J.Y.-T. Leung, Online scheduling of precedence constrained tasks, SIAM Journal on Computing, 34 (2005), 743-762] proved that it is impossible to have an online algorithm of a competitive ratio 1. We provide a best possible online algorithm of competitive ratio 13-12.