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A 3/2-Approximation Algorithm for the Graph Balancing Problem with Two Weights

Department of Computer Science, Western University, London, ON N6A5B7, Canada
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Academic Editor: Jesper Jansson
Algorithms 2016, 9(2), 38; https://doi.org/10.3390/a9020038
Received: 29 April 2016 / Revised: 27 May 2016 / Accepted: 2 June 2016 / Published: 8 June 2016
In the pursuit of finding subclasses of the makespan minimization problem on unrelated parallel machines that have approximation algorithms with approximation ratio better than 2, the graph balancing problem has been of current interest. In the graph balancing problem each job can be non-preemptively scheduled on one of at most two machines with the same processing time on either machine. Recently, Ebenlendr, Krčál, and Sgall (Algorithmica 2014, 68, 62–80.) presented a 7 / 4 -approximation algorithm for the graph balancing problem. Let r , s Z + . In this paper we consider the graph balancing problem with two weights, where a job either takes r time units or s time units. We present a 3 / 2 -approximation algorithm for this problem. This is an improvement over the previously best-known approximation algorithm for the problem with approximation ratio 1.652 and it matches the best known inapproximability bound for it. View Full-Text
Keywords: approximation algorithms; scheduling; graph balancing problem; restricted assignment problem; makespan minimization approximation algorithms; scheduling; graph balancing problem; restricted assignment problem; makespan minimization
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Page, D.R.; Solis-Oba, R. A 3/2-Approximation Algorithm for the Graph Balancing Problem with Two Weights. Algorithms 2016, 9, 38.

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