A Tighter Analysis of Work Stealing

Abstract

Abstract. Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel platforms. However, with the increasing number of processors, the cost for managing a single centralized list becomes prohibitive. The objective of this work is to study the extra cost that must be paid when the list is distributed among the processors. We present a general methodology for computing the expected makespan based on the analysis of an adequate potential function which represents the load unbalance between the local lists. A bound on the deviation from the mean is also derived. Then, we apply this technique to show that the expected makespan for scheduling W unit independent tasks on m processors is equal to W/m with an additional term in 3.65 log 2 W . Moreover, simulations show that our bound is very close to the exact value, approximately 50% off. This new analysis also enables to study the influence of the initial repartition of tasks and the reduction of the number of steals when several thieves can simultaneously steal work in the same processor's list.

X-kaapi: A Multi Paradigm Runtime for Multicore Architectures

“…X-KAAPI favors request aggregation [17]: N pending requests from N thieves to a same victim are handled in one operation, reducing the number of ready task detections. A theoretical analysis in [26] shows a reduction of the total steal request number. In our protocol, one of the thieves is elected to reply to all requests.…”

“…The main thief tries to split [b t , e) into k + 1 equal slices, leaving one slice for the victim. Then, for each of the k requests, the thief returns approximately the same amount of work for balancing purpose [26].…”

Victim Selection and Distributed Work Stealing Performance: A Case Study

“…Indeed, traditional work stealing assumes that victims are selected following an uniform random distribution. Most theoretical proofs of the efficiency of work stealing also rely on this assumption [1], [3]. However, all the implementations provided in the public source code release of UTS use a deterministic scheme.…”

Decentralized list scheduling

“…One can show that r/(−m log 2 h(r)) is increasing in r (see Apx.B of Tchiboukdjian et al (2010) for details). Thus its maximum is attained for r = m. This shows that…”