A _(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks

Abstract

In this paper we study a scheduling problem with moldable and non-moldable parallel tasks on m processors. A non-moldable parallel task is one that runs in parallel on a specific given number of processors. The goal is to find a non-preemptive schedule on the m processors which minimizes the makespan, or the latest task completion time. The previous best result is the list scheduling algorithm with an absolute approximation ratio of 2. On the other hand, there does not exist an approximation algorithm for scheduling non-moldable parallel tasks with ratio smaller than 1.5, unless P = N P . In this paper we show that a schedule with length (1.5 + ǫ)OP T can be computed for the scheduling problem in time O(n log n) + f (1/ǫ). Furthermore we present an (1.5 + ǫ) approximation algorithm for scheduling moldable parallel tasks.

Linear Time Algorithms for Multiple Cluster Scheduling and Multiple Strip Packing

“…We can use this algorithm to find a schedule on the two clusters C 1 and C 2 needed for the algorithm in Section 2. It is inspired by the algorithm in [11] but contains some improvements. Furthermore, note the fact that in the following algorithm the processing times of the jobs do not have to be integral.…”

“…We will now present a more detailed approach. We use an improved rounding strategy for large jobs compared to [11], which enables us to improve the running time. Further, we present a different linear programming approach to schedule the narrow tall jobs.…”

Scheduling Monotone Moldable Jobs in Linear Time

“…algorithms with a running time polynomial in log m. Such algorithms will outperform algorithms whose running time is polynomial in m for large values of m (super-polynomial in the input size). Only few known algorithms are fully polynomial in this sense [20,23,9]. Since we do not want to stipulate a certain form of speedup functions, we assume that the running times t j (k) can be accessed via some oracle in constant time.…”

“…A PTAS with running time polynomial in m was subsequently developed that does not require monotony [14]. Finally, a ( 3 2 + ε)approximate algorithm with polylogarithmic dependence on m that also does not assume monotone jobs was developed by Jansen [9].…”

“…Combine solutions for (I \ I c , ∅, β(α), 0) and (I c , I c ,α, ρ)9 return the best combined solution Theorem 15. Algorithm 2 finds a solution to the instance (I,I c , C, ρ ′ ) with profit at least OPT(I, ∅, C, 0) in time O(n I β max + n Cn ′ log C α min ).…”