Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2

In this paper we study variants of the non-preemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + ε)OPT can be calculated in polynomial time. Unless P = NP, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case, where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most (1.5 + ε)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios

A moldable online scheduling algorithm and its application to parallel short sequence mapping

Abstract. A crucial step in DNA sequence analysis is mapping short sequences generated by next-generation instruments to a reference genome. In this paper, we focus on efficient online scheduling of multi-user parallel short sequence mapping queries on a multiprocessor system. With the availability of parallel execution models, the problem at hand becomes a moldable task scheduling problem where the number of processors needed to execute a task is determined by the scheduler. We propose an online scheduling algorithm to minimize the stretch of the tasks in the system. This metric provides improved fairness to small tasks compared to flow time metric and suits well to the nature of the problem. Experimental evaluation on two workload scenarios indicate that the algorithm results in significantly smaller stretch compared to a recent algorithm and it is more fair to small sized tasks.