Decentralized List Scheduling

TL;DR

This paper investigates decentralized list scheduling for parallel processing, analyzing the additional costs and performance guarantees when distributing the task list among processors, and provides bounds and experimental validation.

Contribution

It introduces a general methodology to analyze distributed list scheduling, deriving bounds on makespan and improving existing results for various task models.

Findings

Scheduling time for independent tasks is W/m plus a log W term.

The additional scheduling cost is proportional to log W, which is shown to be optimal.

Simulations confirm the theoretical bounds and distribution of makespan.

Abstract

Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single centralized list becomes too prohibitive. A suitable approach to reduce the contention is to distribute the list among the computational units: each processor has only a local view of the work to execute. Thus, the scheduler is no longer greedy and standard performance guarantees are lost. The objective of this work is to study the extra cost that must be paid when the list is distributed among the computational units. We first 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. We obtain an equation on the evolution of the potential by computing its expected decrease in one step of the schedule. Our main theorem shows how to solve such equations to bound the makespan. Then, we apply this method to several scheduling problems, namely, for unit independent tasks, for weighted independent tasks and for tasks with precendence constraints. More precisely, we prove that the time for scheduling a global workload W composed of independent unit tasks on m processors is equal to W/m plus an additional term proportional to log_2 W. We provide a lower bound which shows that this is optimal up to a constant. This result is extended to the case of weighted independent tasks. In the last setting, precedence task graphs, our analysis leads to an improvement on the bound of Arora et al. We finally provide some experiments using a simulator. The distribution of the makespan is shown to fit existing probability laws. The additive term is shown by simulation to be around 3 \log_2 W confirming the tightness of our analysis.