Guest editorial

New trends on scheduling in parallel anddistributed systems

Parallel processing is believed to bring computers' power to a new and yet un-precedented level. However, raw processing speed of parallel processors may remainonly an unexploited potential if it is not wisely harnessed by software systems. Thismeans, for example, that parts of parallel applications should not wait for executionlonger than necessary. In other words, resources of parallel systems must be properlymanaged for e�cient program execution. This kind of managing resources is termedscheduling, which can be broadly understood as allocating resources over time toperform tasks being parts of processes. In particular, as processors, being the reasonfor parallelism, are the source of the processing power, carefully managing them is ofcrucial importance for the e�ciency of parallel systems. In contemporary parallelarchitectures and in distributed systems, processors or machines are spatially dis-tributed and communicate via various kinds of interconnections. Therefore, thecommunication medium is another important resource.

Problems of this kind were the topic of the seminar on ``New Trends on Sched-uling in Parallel and Distributed Systems'', held in Aussois, France, from 15 to 19June 1998. During the seminar, the idea was raised to publish some of the interestingpresentations from the area of task scheduling in parallel and distributed systems inthis special issue.

Over 45 participants presented results from the area of task scheduling, mainlyunder consideration of communication delays. Altogether we received 14 highquality submissions for publication, and we were able to accept eight of them for thespecial issue.

Four papers deal with task scheduling under consideration of communicationdelays. Three of them adopt the LogP communication model. The LogP modelcharacterizes a parallel computer system by four parameters: the latency L, theoverhead o, the gap g, and the number of processors P. The ®rst paper (J. Verriet)discusses the complexity of scheduling under speci®c precedence constraints, struc-tured as out-trees. It is proved that constructing minimum-length schedules for forkgraphs (a subclass of out trees) is a strongly NP-hard optimization problem.Moreover, the possibility of using polynomial time algorithms is discussed. Thesecond paper (W. L�owe and W. Zimmermann) deals with the performance of ap-proximation algorithms for scheduling more general precedence graphs on LogPmachines. These algorithms depend on the granularity, i.e., on the ratio of compu-tation r�v� and communication times. For special classes of task graphs with

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applications in fast Fourier transformation, stencil computations to solve partialdi�erential equations, and matrix multiplication, performance bounds of approxi-mation algorithms for coarse-grained and ®ne-grained graphs are presented. Thethird paper (T. Kalinowski, I. Kort and D. Trystram) presents and analyzes ageneral list-scheduling algorithm for any precedence graph under the LogP model.Two adaptations of the earliest task ®rst (ETF) heuristic are presented and an upperbound on list schedules under LogP is established. Finally, extensive experimentalstudies for di�erent graph classes and model instances are performed. The paper ofCh. Lahlou establishes complexity results for the scheduling of tasks with tree-likeprecedences and under unit execution times and unit communication times on anunbounded number of processors. An approximation algorithm for the makespanminimization problem is given when the processors are interconnected by a singlebus. This algorithm is compared with other algorithms by simulations.

The next two papers consider cyclic scheduling problems occurring in ®ne grainparallelism techniques for nested loops. The paper by Ph. Chr�etienne addresses theperformance of list algorithms for scheduling cyclic non-preemptive dependent taskson m identical processors. The reduced precedence graph is assumed to be stronglyconnected but the number of simultaneously active instances of a generic task is notrestricted by one. Firstly, some properties on arbitrary schedules are given. Then, abound for the average cycle time of any regular list schedule is derived which issimilar to the well-known Graham �2ÿ 1=m� bound for non-cyclic scheduling andshows to what extent regular list schedules take the parallelism of the cyclic tasksystem into account. The other paper (A. Darte) deals with the re-organization of aprogram, where loops are combined into a single one. It is used in parallelizingcompilers mainly for increasing the granularity of loops and for improving datareuse. The goal of this paper is to study, from a theoretical point of view, severalvariants of the loop fusion problem ± identifying polynomially solvable cases andNP-complete cases ± and to make the link between these problems and somescheduling problems that arise from completely di�erent areas.

The last two papers deal with di�erent aspects of scheduling respectively staticand dynamic jobs. The ®rst paper (J. Bøa_zewicz, M. Drozdowski, P. Formanowicz,W. Kubiak, G. Schmidt) considers preemptable tasks scheduled on parallel pro-cessors with limited availability. It is well known that in the majority of cases theproblem of preemptive task scheduling on m parallel identical processors with theobjective of minimizing makespan can be solved in polynomial time. In the paper,this problem is generalized to cover the case of parallel processors, which areavailable in certain time intervals only. It is shown that this problem becomes NP-hard in the strong sense in case of trees and identical processors. If tasks form chainsand are processed by identical processors with a staircase pattern of availability, thenthe problem can be solved in low-order polynomial time for Cmax criterion, and alinear programming approach is required for Lmax criterion. Network ¯ow andlinear programming approaches are proposed for independent tasks scheduled on,respectively, uniform and unrelated processors with arbitrary patterns of availabilityfor schedule length and maximum lateness criteria. The second paper (L.M. Campos,I.D. Scherson) proposes a new strategy for balancing the load of dynamically

1062 Guest editorial / Parallel Computing 26 (2000) 1061±1063

arriving jobs. Dynamic load balancing is an important system function destined todistribute workload among available processors to improve throughput and/or ex-ecution times of parallel computer programs either uniform or non-uniform (jobswhose workload varies at run-time in unpredictable ways). Non-uniform computa-tion and communication requirements may bog down a parallel computer if no ef-®cient load distribution is e�ected. A novel distributed algorithm for load balancingis proposed which is based on local rate of change observations rather than on globalabsolute load numbers. It is a totally distributed algorithm and requires no cen-tralized trigger and/or decision makers. The strategy is discussed and analyzed bymeans of experimental simulation.

Editing this issue of Parallel Computing would not have been possible without thehelp of the referees, and we appreciate their careful evaluation of the submittedpapers. Special thanks are due to Gerhard Joubert and Denis Trystram for theirencouragement during the preparation of this volume.

11 February 2000 Jacek Bøa _zewicz

Institute of Computing SciencePoznan University of Technology

Poznan, Poland

Klaus H. EckerInstit�ut f�ur Informatik

Technische Universit�at ClausthalJulius Albert Str. 4, 38678

Clausthal, GermanyE-mail addresses: ecker@informatik.tu-clausthal.de

ecker@zaphod.in.tu-clausthal.de

Tao Yang

Computer Science DepartmentUniversity of California

Santa Barbara, CA 93106, USA

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