Yu-Kwong Kwok

Static scheduling algorithms for allocating directed task graphs to multiprocessors

Static scheduling of a program represented by a directed task graph on a multiprocessor system to minimize the program completion time is a well-known problem in parallel processing. Since finding an optimal schedule is an NP-complete problem in general, researchers have resorted to devising efficient heuristics. A plethora of heuristics have been proposed based on a wide spectrum of techniques, including branch-and-bound, integer-programming, searching, graph-theory, randomization, genetic algorithms, and evolutionary methods. The objective of this survey is to describe various scheduling algorithms and their functionalities in a contrasting fashion as well as examine their relative merits in terms of performance and time-complexity. Since these algorithms are based on diverse assumptions, they differ in their functionalities, and hence are difficult to describe in a unified context. We propose a taxonomy that classifies these algorithms into different categories. We consider 27 scheduling algorithms, with each algorithm explained through an easy-to-understand description followed by an illustrative example to demonstrate its operation. We also outline some of the novel and promising optimization approaches and current research trends in the area. Finally, we give an overview of the software tools that provide scheduling/mapping functionalities.

Dynamic critical-path scheduling: an effective technique for allocating task graphs to multiprocessors

In this paper, we propose a static scheduling algorithm for allocating task graphs to fully connected multiprocessors. We discuss six recently reported scheduling algorithms and show that they possess one drawback or the other which can lead to poor performance. The proposed algorithm, which is called the Dynamic Critical-Path (DCP) scheduling algorithm, is different from the previously proposed algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it selects a suitable processor for a node by looking ahead the potential start times of the remaining nodes on that processor, and schedules relatively less important nodes to the processors already in use. A global as well as a pair-wise comparison is carried out for all seven algorithms under various scheduling conditions. The DCP algorithm outperforms the previous algorithms by a considerable margin. Despite having a number of new features, the DCP algorithm has admissible time complexity, is economical in terms of the number of processors used and is suitable for a wide range of graph structures.

Trusted P2P transactions with fuzzy reputation aggregation

Internet commerce and online commodity exchanges suffer from distrust among sellers and buyers, who are often strangers to each other. The authors present a new P2P reputation system based on fuzzy logic inferences, which can better handle uncertainty, fuzziness, and incomplete information in peer trust reports. This system aggregates peer reputations with affordable message overhead. By testing the system using eBay transaction data in the public domain, the authors seek to demonstrate the efficacy and robustness of two P2P reputation systems - fuzzytrust and eigentrust - at establishing trust among the peers in P2P applications.

Benchmarking and Comparison of the Task Graph Scheduling Algorithms

The problem of scheduling a parallel program represented by a weighted directed acyclic graph (DAG) to a set of homogeneous processors for minimizing the completion time of the program has been extensively studied. The NP-completeness of the problem has stimulated researchers to propose a myriad of heuristic algorithms. While most of these algorithms are reported to be efficient, it is not clear how they compare against each other. A meaningful performance evaluation and comparison of these algorithms is a complex task and it must take into account a number of issues. First, most scheduling algorithms are based upon diverse assumptions, making the performance comparison rather meaningless. Second, there does not exist a standard set of benchmarks to examine these algorithms. Third, most algorithms are evaluated using small problem sizes, and, therefore, their scalability is unknown. In this paper, we first provide a taxonomy for classifying various algorithms into distinct categories according to their assumptions and functionalities. We then propose a set of benchmarks that are based on diverse structures and are not biased toward a particular scheduling technique. We have implemented 15 scheduling algorithms and compared them on a common platform by using the proposed benchmarks, as well as by varying important problem parameters. We interpret the results based upon the design philosophies and principles behind these algorithms, drawing inferences why some algorithms perform better than others. We also propose a performance measure called scheduling scalability (SS) that captures the collective effectiveness of a scheduling algorithm in terms of its solution quality, the number of processors used, and the running time.

On exploiting task duplication in parallel program scheduling

One of the main obstacles in obtaining high performance from message-passing multicomputer systems is the inevitable communication overhead which is incurred when tasks executing on different processors exchange data. Given a task graph, duplication-based scheduling can mitigate this overhead by allocating some of the tasks redundantly on more than one processor. In this paper, we focus on the problem of using duplication in static scheduling of task graphs on parallel and distributed systems. We discuss five previously proposed algorithms and examine their merits and demerits. We describe some of the essential principles for exploiting duplication in a more useful manner and, based on these principles, propose an algorithm which outperforms the previous algorithms. The proposed algorithm generates optimal solutions for a number of task graphs. The algorithm assumes an unbounded number of processors. For scheduling on a bounded number of processors, we propose a second algorithm which controls the degree of duplication according to the number of available processors. The proposed algorithms are analytically and experimentally evaluated and are also compared with the previous algorithms.

Risk-resilient heuristics and genetic algorithms for security-assured grid job scheduling

In scheduling a large number of user jobs for parallel execution on an open-resource grid system, the jobs are subject to system failures or delays caused by infected hardware, software vulnerability, and distrusted security policy. This paper models the risk and insecure conditions in grid job scheduling. Three risk-resilient strategies, preemptive, replication, and delay-tolerant, are developed to provide security assurance. We propose six risk-resilient scheduling algorithms to assure secure grid job execution under different risky conditions. We report the simulated grid performances of these new grid job scheduling algorithms under the NAS and PSA workloads. The relative performance is measured by the total job makespan, grid resource utilization, job failure rate, slowdown ratio, replication overhead, etc. In addition to extending from known scheduling heuristics, we developed a new space-time genetic algorithm (STGA) based on faster searching and protected chromosome formation. Our simulation results suggest that, in a wide-area grid environment, it is more resilient for the global job scheduler to tolerate some job delays instead of resorting to preemption or replication or taking a risk on unreliable resources allocated. We find that delay-tolerant min-min and STGA job scheduling have 13-23 percent higher performance than using risky or preemptive or replicated algorithms. The resource overheads for replicated job scheduling are kept at a low 15 percent. The delayed job execution is optimized with a delay factor, which is 20 percent of the total makespan. A Kiviat graph is proposed for demonstrating the quality of grid computing services. These risk-resilient job scheduling schemes can upgrade grid performance significantly at only a moderate increase in extra resources or scheduling delays in a risky grid computing environment

Benchmarking the task graph scheduling algorithms

The problem of scheduling a weighted directed acyclic graph (DAG) to a set of homogeneous processors to minimize the completion time has been extensively studied. The NP-completeness of the problem has instigated researchers to propose a myriad of heuristic algorithms. While these algorithms are individually reported to be efficient, it is not clear how effective they are and how well they compare against each other. A comprehensive performance evaluation and comparison of these algorithms entails addressing a number of difficult issues. One of the issues is that a large number of scheduling algorithms are based upon radically different assumptions, making their comparison on a unified basis a rather intricate task. Another issue is that there is no standard set of benchmarks that can be used to evaluate and compare these algorithms. Furthermore, most algorithms are evaluated using small problem sizes, and it is not clear how their performance scales with the problem size. The authors first provide a taxonomy for classifying various algorithms into different categories according to their assumptions and functionalities. They then propose a set of benchmarks which are of diverse structures without being biased towards a particular scheduling technique and still allow variations in important parameters. They have evaluated 15 scheduling algorithms, and compared them using the proposed benchmarks. Based upon the design philosophies and principles behind these algorithms, they interpret the results and discuss why some algorithms perform better than the others.

Efficient Scheduling of Arbitrary Task Graphs to Multiprocessors Using a Parallel Genetic Algorithm

Given a parallel program represented by a task graph, the objective of a scheduling algorithm is to minimize the overall execution time of the program by properly assigning the nodes of the graph to the processors. This multiprocessor scheduling problem is NP-complete even with simplifying assumptions and becomes more complex under relaxed assumptions such as arbitrary precedence constraints, and arbitrary task execution and communication times. The present literature on this topic is a large repertoire of heuristics that produce good solutions in a reasonable amount of time. These heuristics, however, have restricted applicability in a practical environment because they have a number of fundamental problems including high time complexity, lack of scalability, and no performance guarantee with respect to optimal solutions. Recently, genetic algorithms (GAs) have been widely reckoned as a useful vehicle for obtaining high quality or even optimal solutions for a broad range of combinatorial optimization problems. While a few GAs for scheduling have already been suggested, in this paper we propose a novel GA-based algorithm with an objective to simultaneously meet the goals of high performance, scalability, and fast running time. The proposed parallel genetic scheduling (PGS) algorithm itself is a parallel algorithm which generates high quality solutions in a short time. By encoding the scheduling list as a chromosome, the PGS algorithm can potentially generate an optimal scheduling list which in turn leads to an optimal schedule. The major strength of the PGS algorithm lies in its two efficient genetic operators: the order crossover and mutation. These operators effectively combine the building-blocks of good scheduling lists to construct better lists. The proposed algorithm is evaluated through a robust comparison with two heuristics best known in terms of performance and time complexity. It outperforms both heuristics while taking considerably less running time. When evaluated with random task graphs for which optimal solutions are known, the PGS algorithm generates optimal solutions for more than half of the test cases and close-to-optimal for the other half.

A New Approach to Scheduling Parallel Programs Using Task Duplication

In this paper, we explore the problem of scheduling parallel programs using task duplication for message-passing multicomputers. Task duplication means scheduling a parallel program by redundantly executing some of the tasks on which other tasks of the program critically depend. This can reduce the start times of tasks waiting for messages from tasks residing in other processors. There have been a few scheduling algorithms using task duplication. We discuss two such previously reported algorithms and describe their differences, limitations and suitability for different environments. A new algorithm is proposed which outperforms both of these algorithms, and is more efficient for low as well as high values of communication-to-computation ratios. The algorithm takes into account arbitrary computation and communication costs. All three algorithms are tested by scheduling some of the commonly encountered graph structures.

Analysis, evaluation, and comparison of algorithms for scheduling task graphs on parallel processors

In this paper, we survey algorithms that allocate a parallel program represented by an edge-weighted directed acyclic graph (DAG), also called a task graph or macro-dataflow graph, to a set of homogeneous processors, with the objective of minimizing the completion time. We analyze 21 such algorithms and classify them into four groups. The first group includes algorithms that schedule the DAG to a bounded number of processors directly. These algorithms are called the bounded number of processors (BNP) scheduling algorithms. The algorithms in the second group schedule the DAG to an unbounded number of clusters and are called the unbounded number of clusters (UNC) scheduling algorithms. The algorithms in the third group schedule the DAG using task duplication and are called the task duplication based (TDB) scheduling algorithms. The algorithms in the fourth group perform allocation and mapping on arbitrary processor network topologies. These algorithms are called the arbitrary processor network (APN) scheduling algorithms. The design philosophies and principles behind these algorithms are discussed, and the performance of all of the algorithms is evaluated and compared against each other on a unified basis by using various scheduling parameters.