Online Non-preemptive Scheduling of Equal-length Jobs on Two Identical Machines

by Michael H. Goldwasser and Mark Pedigo


We consider the non-preemptive scheduling of two identical machines for jobs with equal processing times yet arbitrary release dates and deadlines. Our objective is to maximize the number of jobs completed by their deadlines. Using standard nomenclature, this problem is denoted as P2 | pj=p, rj | Σ Ūj. The problem is known to be polynomially solvable in an offline setting.

In an online variant of the problem, a job's existence and parameters are revealed to the scheduler only upon that job's release date. We present an online deterministic algorithm for the problem and prove that it is 3/2-competitive. A simple lower bound shows that this is the optimal deterministic competitiveness.

Online Nonpreemptive Scheduling of Equal-Length Jobs on Two Identical Machines
Michael H. Goldwasser and Mark Pedigo
Proceedings of the Tenth Scandinavian Workshop on Algorithm Theory (SWAT), Riga, Latvia, volume 4059 of Lecture Notes in Computer Science (Springer-Verlag, Berlin), Jul. 2006, pp. 113-123.
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A complete version later appeared in:
ACM Transactions on Algorithms, 5(1), 2008
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Michael Goldwasser