Task scheduling in multiprocessing systems

Citeseer

We study the off and on-line versions of the well known problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a set of identical processors in order to minimize the makespan. Recently, in [12], it has been proven that in the case when all tasks have unit processing time the problem cannot be approximated within a factor of m 1– ∈, neither for some ∈ > 0, unless P= NP; nor for any ∈ > 0, unless NP=ZPP. For this special case we give a simple algorithm based on the classical first-fit technique. We analyze the algorithm for both tasks arrive over time and tasks arrive over list on-line scheduling versions, and show that its competitive ratio is bounded by 2√m and 2√m + 1, respectively. Here we also use some preliminary results on (vertex) coloring of k-tuple graphs. For the case of arbitrary processing times, we show that any algorithm which uses the first-fit technique cannot be better than m competitive. Then, by using our split-round technique, we give a 3√m-approximation algorithm for the off-line version of the problem. Finally, by using some ideas from [20], we adapt the algorithm to the on-line case, in the paradigm of tasks arriving over time in which the existence of a task is unknown until its release date, and show that its competitive ratio is bounded by 6√m. Due to the conducted experimental results, we conclude that our algorithms can perform well in practice.

IEEE Transactions on Computers, 1986

The problem considered in this paper is the deterministic scheduling of tasks on a set of identical processors. However, the model presented differs from the classical one by the requirement that certain tasks need more than one proc9essor at a time for their processing. This assumption is especially justifidd in some microprocessor applications and its impact on the complexity of minimizing schedule length is studied. First we concentrate on the problem of nonpreemptive scheduling. In this case, polynomial-time algorithms exist only for unit processing times. We present two such algorithms of complexity O(n) for scheduling tasks requiring an arbitrary number of processors between 1 and k at a time where k is a fixed integer. The case for which k is not fixed is shown to be NP-complete. Next, the problem of preemptive scheduling of tasks of arbitrary length is studied. First an algorithm for scheduling tasks requiring one or k processors is presented. Its complexity depends linearly on the number of tasks. Then, the possibility of a linear programming formulation for the general case is analyzed. Index Terms-Complexity analysis, deterministic scheduling, linear programming approach, microprocessor systems, polynomial-in-time algorithms, preemptive and nonpreemptive schedules, schedule length criterion, scheduling multiprocessor tasks. 'We assume that the reader is familiar with the general concepts of the NP-completeness theory which may be found, for example, in [10].

1997

We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of length within a factor of (1+ c) of optimal in the non-preemptive model.

Proceedings 11th International Parallel Processing Symposium, 1997

This paper demonstrates the effectiveness of the twophase method of scheduling, in which task clustering is performed prior to the actual scheduling process. Task clustering determines the optimal or near-optimal number of processors on which to schedule the task graph. In other words, there is never a need to use more processors (even though they are available) than the number of clusters produced by the task clustering algorithm. The paper also indicates that when task clustering is performed prior to scheduling, load balancing (LB) is the preferred approach for cluster merging. LB is fast, easy to implement, and produces significantly better final schedules than communication traffic minimizing (CTM). In summary, the two-phase method consisting of task clustering and load balancing is a simple yet highly effective strategy for scheduling task graphs on distributed memory parallel architectures.

ACM SIGARCH Computer Architecture News, 1984

The paper describes a technique for estimating the minimum execution time of an algorithm or a mix of algorithms on a distributed processing system. Bottlenecks that would have to be removed to further reduce the execution time are identified. The main applications are for the high level design of special purpose distributed processing systems. The distributed systems are modelled by P, a set of nonidentical processors and R, a set of resources that the processors can use. The algorithms are modelled by T, an ordered set of tasks. The problem of optimally assigning the processors to the tasks while meeting the resource constraints is NP-complete. However, a heuristic using maximum weighted matchings on graphs has been devised that is extremely fast and comes reasonably close to the optimal solutions.

Discrete Applied Mathematics, 1996

In the classical scheduling theory it is widely assumed that any task requires for its processing only one processor at a time. Nowadays with the technological progress this assumption has become not so obvious. In the paper, two algorithms for solving the problem of scheduling tasks requiring more than one processor at a time in the real-time environment, will be given. The first is based on a generation of all feasible layouts of tasks and on an application of linear programming. The second heuristic one is based on the descent search in solution space and the tabu search metaheuristic combined with linear programming. Results of a computational comparison of the two methods, are also reported. 'The research has been partially supported by KBN grant.

Real-time Systems, 1997

A heuristic approach to the problem of assigning a set of preemptible resource-sharing and blockable real-time tasks to be executed in a set of heterogeneous processors communicated through an interprocessor network, is presented. The problem is NP-hard. The empty-slots method is used to test the RM schedulability in each processor. There are placement, time, memory, communication and precedence constraints. A general expression for the modification of hard-precedence deadlines of related tasks executing in the same or in different processors is given. The effects of the Average Processor Utilization Factor and the Network Bandwidth on the number of solutions found are shown and discussed through systematic sets of examples. Also, Success Ratios are obtained and plotted vs. Average Processor Utilization Factors for different Network Bandwidths. Results obtained are compared to those obtained by other methods.

2007

Scheduling theory is concerned with the optimal allocation of scarce resources (for instance, machines, processors, robots, operators, etc.) to activities over time, with the objective of optimizing one or several performance measures. The study of scheduling started about fifty years ago, being initiated by seminal papers by and Bellman (1956). Since then machine scheduling theory have received considerable development. As a result, a great diversity of scheduling models and optimization techniques have been developed that found wide applications in industry, transport and communications. Today, scheduling theory is an integral, generally recognized and rapidly evolving branch of operations research, fruitfully contributing to computer science, artificial intelligence, and industrial engineering and management. The interested reader can find many nice pearls of scheduling theory in textbooks, monographs and handbooks by Tanaev et al. (1994a,b), Pinedo (2001), Leung (2001), Brucker (2007, and Blazewicz et al. (2007). This book is the result of an initiative launched by Prof. Vedran Kordic, a major goal of which is to continue a good tradition -to bring together reputable researchers from different countries in order to provide a comprehensive coverage of advanced and modern topics in scheduling not yet reflected by other books. The virtual consortium of the authors has been created by using electronic exchanges; it comprises 50 authors from 18 different countries who have submitted 23 contributions to this collective product. In this sense, the volume in your hands can be added to a bookshelf with similar collective publications in scheduling, started by Coffman (1976) and successfully continued by Chretienne et al. (1995), Gutin and Punnen (2002), and Leung (2004). This volume contains four major parts that cover the following directions: the state of the art in theory and algorithms for classical and non-standard scheduling problems; new exact optimization algorithms, approximation algorithms with performance guarantees, heuristics and metaheuristics; novel models and approaches to scheduling; and, last but least, several real-life applications and case studies. The brief outline of the volume is as follows. Part I presents tutorials, surveys and comparative studies of several new trends and modern tools in scheduling theory. Chapter 1 is a tutorial on theory of cyclic scheduling. It is included for those readers who are unfamiliar with this area of scheduling theory. Cyclic scheduling models are traditionally used to control repetitive industrial processes and enhance the performance of robotic lines in many industries. A brief overview of cyclic scheduling models arising in manufacturing systems served by robots is presented, started with a discussion of early works appeared in the 1960s. Although the considered scheduling problems are, in general, NP-hard, a graph approach presented in this chapter permits to reduce some special cases to the parametric critical path problem in a graph and solve them in polynomial time. Chapter 2 describes the so-called multi-agent scheduling models applied to the situations in which the resource allocation process involves different stakeholders ("agents"), each having his/her own set of jobs and interests, and there is no central authority which can VI solve possible conflicts in resource usage over time. In this case, standard scheduling models become invalid, since rather than computing "optimal solutions", the model is asked to provide useful elements for the negotiation process, which eventually should lead to a stable and acceptable resource allocation. The chapter does not review the whole scope in detail, but rather concentrates on combinatorial models and their applications. Two major mechanisms for generating schedules, auctions and bargaining models, corresponding to different information exchange scenarios, are considered. Known results are reviewed and venues for future research are pointed out. Chapter 3 considers a class of scheduling problems under unavailability constraints associated, for example, with breakdown periods, maintenance durations and/or setup times. Such problems can be met in different industrial environments in numerous real-life applications. Recent algorithmic approaches proposed to solve these problems are presented, and their complexity and worst-case performance characteristics are discussed. The main attention is devoted to the flow-time minimization in the weighted and unweighted cases, for single-machine and parallel machine scheduling problems. Chapter 4 is devoted to the analysis of scheduling problems with communication delays. With the increasing importance of parallel computing, the question of how to schedule a set of precedence-constrained tasks on a given computer architecture, with communication delays taken into account, becomes critical. The chapter presents the principal results related to complexity, approximability and non-approximability of scheduling problems in presence of communication delays. Part II comprising eight chapters is devoted to the design of scheduling algorithms. Here the reader can find a wide variety of algorithms: exact, approximate with performance guarantees, heuristics and meta-heuristics; most algorithms are supplied by the complexity analysis and/or tested computationally. Chapter 5 deals with a batch version of the single-processor scheduling problem with batch setup times and batch delivery costs, the objective being to find a schedule which minimizes the sum of the weighted number of late jobs and the delivery costs. A new dynamic programming (DP) algorithm which runs in pseudo-polynomial time is proposed. By combining the techniques of binary range search and static interval partitioning, the DP algorithm is converted into a fully polynomial time approximation scheme for the general case. The DP algorithm becomes polynomial for the special cases when jobs have equal weights or equal processing times. Chapter 6 studies on-line approximation algorithms with performance guarantees for an important class of scheduling problems defined on identical machines, for jobs with arbitrary release times. Chapter 7 presents a new hybrid metaheuristic for solving the jobshop scheduling problem that combines augmented-neural-networks with genetic algorithm based search. In Chapter 8 heuristics based on a combination of the guided search and tabu search are considered to minimize the maximum completion time and maximum tardiness in the parallel-machine scheduling problems. Computational characteristics of the proposed heuristics are evaluated through extensive experiments. Chapter 9 presents a hybrid meta-heuristics based on a combination of the genetic algorithm and the local search aimed to solve the re-entrant flowshop scheduling problems. The hybrid method is compared with the optimal solutions generated by the integer programming technique, and the near optimal solutions generated by a pure genetic algorithm. Computational experiments are performed to illustrate the effectiveness and efficiency of the proposed algorithm.

2019

The main purpose of task scheduling is to assign tasks onto available processors with the aim of producing minimum schedule length and without violating the precedence constraints. In heterogeneous multiprocessing systems, task assignments and scheduling have a great impact on the system operation. In a heuristic based task scheduling algorithm, different process will result different task execution time (makespan) on a heterogeneous computing system. Thus, a good scheduling algorithm should be capable to efficiently assign precedence to each subtask depending on the resources required to reduce makespan. In this report, we propose a genetic algorithm (PGA) to resolve a task assignment and scheduling for homogeneous and heterogeneous multi-processing problem. The basic idea of this process is to exploit the advantages of heuristic-based algorithms to decrease space search and the time needed to get the best solution. The achieved results show that the suggested approach significantl...

I One of the key problems in the design of any incompletely connected multiprocessor system is to appropriately assign the set of tasks in a program to the Processing Elements (PEs) in the system. The task assignment problem has proven difficult both in theory and in practice. This paper presents a simple and efficient heuristic algorithm for assigning program tasks with execution and communication constraints to the PEs in a Message-based Multiple-bus Multiprocessor System, so that the total execution time for the program is minimized. The algorithm uses a cost function: "Minimum Distance and Parallel Transfer" to minimize the completion time. The effectiveness of the algorithm has been demonstrated by comparing the results with (i) the lower bound on the execution time of a program (task) graph and (ii) a random assignment.

Lecture Notes in Computer Science, 2000

Abstract|An algorithm for solving the linear programming problem known as the multiprocessor distribution (or scheduling) problem is suggested. The problem is to distribute a given set of tasks among given processors so as to minimize the load time of the most loaded processor. Dividing the tasks into parts and distributing the parts among di erent processors is allowed. The algorithm constructed uses the speci cs of the multiprocessor distribution problem and can therefore operate substantially more e ciently than the general linear programming algorithm. The author was unable to answer the question about the polynomiality of the algorithm.

Algorithms and …, 2002

Arabian Journal for Science and Engineering, 2016

Parallel computing systems promise higher performance for computationally intensive applications. Since programmes for parallel systems consist of tasks that can be executed simultaneously, task scheduling becomes crucial for the performance of these applications. Given dependence constraints between tasks, their arbitrary sizes, and bounded resources available for execution, optimal task scheduling is considered as an NP-hard problem. Therefore, proposed scheduling algorithms are based on heuristics. This paper presents a novel list scheduling heuristic, called the Noodle heuristic. Noodle is a simple yet effective scheduling heuristic that differs from the existing list scheduling techniques in the way it assigns task priorities. The priority mechanism of Noodle maintains a proportionate fairness among all ready tasks belonging to all paths within a task graph. We conduct an extensive experimental evaluation of Noodle heuristic with task graphs taken from Standard Task Graph. Our experimental study includes results for task graphs comprising of 50, 100, and 300 tasks per graph and execution scenarios with 2-, 4-, 8-, and 16-core systems. We report results for average Schedule Length Ratio (SLR) obtained by producing variations in Communication to Computation cost Ratio. We also analyse results for different degree of parallelism and

Scheduling of a task on a multiprocessor system represented by a directed acyclic graph for minimizing the different performance measures is a prominent problem in parallel processing. As judgment of an optimal schedule for multiprocessor task scheduling problem is a NP hard problem and different researchers have resorted for devising efficient heuristics. List scheduling heuristics belong to one of the categories used for multiprocessor task scheduling problem. Present work considers the comparative analysis of five commonly used list scheduling heuristics based on makespan and total completion time of the schedule for homogeneous multiprocessors. A defined Performance Index (PI) is used for the comparative analysis of different heuristics and it has been proved that the Insertion Scheduling Heuristic (ISH) Algorithm and Earliest Time First (ETF) Algorithm provides the best results for trade-off between the makespan and total completion time of the schedule.

International Journal of Computer Applications, 2012

In multiprocessor system, scheduling of tasks to assigned on the number of processors. The major objective of task scheduling is to find minimum execution time of a program. It is well known that the complexity of a general scheduling problem is NP-Complete [9], there are number of heuristic have been developed. Each of which may either find optimal or near optimal scheduling under the different conditions. The task scheduling is represented by a directed acyclic graph (DAG). In this paper, we present a new scheduling algorithm which is called Task Scheduling based on Breath First Search(TSB). The TSB is queue based approach to schedule parallel tasks on the homogenous parallel multiprocessor system. Its performance is evaluated in comparison with Highest Level First with Estimate Time (HLFET) algorithm, Modified Critical Path (MCP) algorithm, Earliest Time First (ETF) algorithm and Dynamic Level Scheduling (DLS) algorithm in terms of Speedup, Efficiency, Load Balance and Normalized Scheduling Length (NSL).