In this paper we experimentally evaluate the performance of a parametrized branch-and-bound (B&B) algorithm for scheduling real-time tasks on a multiprocessor system. The objective of the B&B algorithm is to minimize the maximum task lateness in the system. We show that a last-in-first-out (LIFO) vertex selection rule clearly outperforms the commonly used least-lower-bound (LLB) rule for the scheduling problem. We also present a new adaptive lower-bound cost function that greatly improves the performance of the B&B algorithm when parallelism in the application cannot be fully exploited on the multiprocessor architecture. Finally, we evaluate a set of heuristic strategies, one of which generates near-optimal results with performance guarantees and another of which generates approximate results without performance guarantees. 1 Introduction Since its introduction in the field of artificial intelligence, the branch-and-bound (B&B) strategy has been successfully used for finding optimal ...

. This paper surveys, analyses and establishes new polynomial-time reductions among scheduling problems that connect identical parallel machines with unit-time shops and the preemption facility with chain-like precedence constraints in equal machine environments. The reductions turn out to be unexpectedly fruitful in clarifying the complexity status of many scheduling problems that were open before. New complexity results in the paper are devoted to identical parallel machines, ow shops and open shops. 1. Introduction Recently found mass polynomial-time reductions between scheduling problems on identical parallel machines and shop scheduling problems with nonpreemptive unit processing time operations proved to be very eective in studying their complexity. The latter problems we simply call unit-time shops. Reductions of unit-time shops to identical parallel machines we call parallelizings, and the inverse reductions, i.e., of identical parallel machines to unittime shops, we c...

In a single-machine problem with time-lags a set of jobs has to be processed on a single machine in such a way that certain timing restrictions between the finishing and starting times of the jobs are satisfied and a given objective function is minimized. We consider the case of positive finishstart time-lags l ij which mean that between the finishing time of job i and the starting time of job j the minimal distance l ij has to be respected. New complexity results are derived for single-machine problems with constant positive time-lags l ij = l which also lead to new results for flow-shop problems with unit processing times and job precedences. Key words: complexity results, time-lags, single machine, flow-shop problem Supported by the Deutsche Forschungsgemeinschaft, Project `Komplexe Maschinen-Schedulingprobleme ' 1 Introduction In a single-machine problem a set of jobs j = 1; : : : ; n has to be processed without preemption on a single machine in such a way that at most one jo...

Automatic tool support for scheduling applications on multiprocessor platforms is of paramount importance both to guarantee critical application demands and to keep development costs down. In this paper, we present GAST, an objectoriented evaluation environment for multiprocessor assignment and scheduling techniques. GAST is based on a decomposition approach where existing assignment and scheduling techniques have been broken down into a set of common operations. By combining these operations into a complete scheduling process, GAST offers a powerful toolbox of existing assignment and scheduling techniques. GAST has been implemented on several popular operating systems and is accompanied by a graphic visualization tool that allows for flexible interaction with the application scheduling process. 1 Introduction For economical reasons, single-processor computers have traditionally been the only viable option for many computer system designers. This has, in turn, limited the sphere of f...

The application of optimal search strategies to scheduling for distributed real-time systems is, in general, plagued by an inherent computational complexity. This has effectively prevented the integration of strategies such as branch-andbound (B&B) in scheduling frameworks and tools used in practice today. To show that optimal scheduling is, in fact, a viable alternative for many real-time scheduling scenarios, we propose an approach that can reduce the average search complexity to levels comparable with that of a polynomialtime heuristic. Our approach is based on making intelligent choices in the selection of strategies for search tree vertex traversal and task deadline assignment. More specifically, we conjecture that effective complexity reduction is achieved by (i) traversing vertices in the search tree in a depth-first fashion and (ii) assigning local task deadlines that are nonoverlapping fractions of the application end-to-end deadline. Through an extensive experimental study, w...

The problem of scheduling precedence graphs for which every task has to be executed in a non-uniform interval is considered, with interprocessor communication delays. For the following classes of graphs we will present a polynomial time algorithm that finds minimumlateness schedules. 1. Outforests on two processors. 2. Series-parallel graphs and opposing forests with the least urgent parent property (to be defined) on two processors. 3. Inforests with the least urgent parent property on m processors.

This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date first algorithm provides an optimal nonpreemptive schedule for unitexecution -time (UET) tasks, then the preemptive priority scheduling algorithm, referred to as Smallest Laxity First, provides an optimal preemptive schedule for real-execution-time (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between Highest Level First schedules solving nonpreemptive tasks with UET and the Longest Remaining Path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained. Keywords: Preemptive Scheduling, List Schedule, Priority Schedule, Variable P...

. This paper considers problems of finding nonperiodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but some of the machines in the route can be met more than once. We propose a classification of cycle shops and show that recently studied reentrant flow shops, robotic flow shops, loop reentrant flowshops and V shops are special cases of cycle shops. Problems solvable in polynomial time, pseudopolynomial time, NP-hard problems and performance guarantee approximations are presented. Related earlier results are surveyed. 1.

AbstractÐSince instruction level parallelism in basic blocks is often limited, compilers increase performance by creating superblocks that allow operations to be issued speculatively. This is difficult in general because each branch competes for the processor's limited resources. Previous work manages the performance trade-offs that exist between branches only indirectly. We show here that dependence and resource constraints can be used to gather explicit knowledge about scheduling trade-offs between branches. This paper's first contribution is a set of new, tighter lower bounds on the execution times of superblocks that specifically account for the dependence and resource conflicts between pairs of branches. This paper's second contribution is a novel superblock scheduling heuristic that finds high performance schedules by determining the operations that each branch needs to be scheduled early and selecting branches with compatible needs that favor beneficial branch trade-offs. Performance evaluations for superblocks from SPECint95 indicate that our bounds are very tight and that our scheduling heuristic outperforms well-known superblock scheduling algorithms. Index TermsÐSuperblock, scheduling heuristic, lower bound, ILP compiler technique. 1

We consider two general precedence-constrained scheduling problems that have wide applicability in the areas of parallel processing, high performance compiling, and digital system synthesis. These problems are intractable so it is important to be able to compute tight bounds on their solutions. A tight lower bound on makespan scheduling can be obtained by replacing precedence constraints with release and due dates, giving a problem that can be efficiently solved. We demonstrate that recursively applying this approach yields a bound that is provably tighter than other known bounds, and experimentally shown to achieve the optimal value at least 86.5% of the time over a synthetic benchmark. We compute the best known lower bound on weighted completion time scheduling by applying the recent discovery of a new algorithm for solving a related scheduling problem. Experiments show that this bound significantly outperforms the linear programming-based bound. We have therefore demonstrated that combinatorial algorithms can be a valuable alternative to linear programming for computing tight bounds on large scheduling problems.