Efficient application scheduling is critical for achieving high performance in heterogeneous computing environments. The application scheduling problem has been shown to be NP-complete in general cases as well as in several restricted cases. Because of its key importance, this problem has been extensively studied and various algorithms have been proposed in the literature which are mainly for systems with homogeneous processors. Although there are a few algorithms in the literature for heterogeneous processors, they usually require significantly high scheduling costs and they may not deliver good quality schedules with lower costs. In this paper, we present two novel scheduling algorithms for a bounded number of heterogeneous processors with an objective to simultaneously meet high performance and fast scheduling time, which are called the Heterogeneous Earliest-Finish-Time (HEFT) algorithm and the Critical-Path-on-a-Processor (CPOP) algorithm. The HEFT algorithm selects the task with the highest upward rank value at each step and assigns the selected task to the processor, which minimizes its earliest finish time with an insertion-based approach. On the other hand, the CPOP algorithm uses the summation of upward and downward rank values for prioritizing tasks. Another difference is in the processor selection phase, which schedules the critical tasks onto the processor that minimizes the total execution time of the critical tasks. In order to provide a robust and unbiased comparison with the related work, a parametric graph generator was designed to generate weighted directed acyclic graphs with various characteristics. The comparison study, based on both randomly generated graphs and the graphs of some real applications, shows that our scheduling algorithms significantly surpass previous approaches in terms of both quality and cost of schedules, which are mainly presented with schedule length ratio, speedup, frequency of best results, and average scheduling time metrics.

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Performance-effective and low-complexity task scheduling for heterogeneous computing

Software fault localization, the act of identifying the locations of faults in a program, is widely recognized to be one of the most tedious, time consuming, and expensive – yet equally critical – activities in program debugging. Due to the increasing scale and complexity of software today, manually locating faults when failures occur is rapidly becoming infeasible, and consequently, there is a strong demand for techniques that can guide software developers to the locations of faults in a program with minimal human intervention. This demand in turn has fueled the proposal and development of a broad spectrum of fault localization techniques, each of which aims to streamline the fault localization process and make it more effective by attacking the problem in a unique way. In this article, we catalog and provide a comprehensive overview of such techniques and discuss key issues and concerns that are pertinent to software fault localization as a whole.

A Survey on Software Fault Localization

Spectrum-based fault localization shortens the test- diagnose-repair cycle by reducing the debugging effort. As a light-weight automated diagnosis technique it can easily be integrated with existing testing schemes. However, as no model of the system is taken into account, its diagnostic accuracy is inherently limited. Using the Siemens Set benchmark, we investigate this diagnostic accuracy as a function of several parameters (such as quality and quantity of the program spectra collected during the execution of the system), some of which directly relate to test design. Our results indicate that the superior performance of a particular similarity coefficient, used to analyze the program spectra, is largely independent of test design. Furthermore, near- optimal diagnostic accuracy (exonerating about 80% of the blocks of code on average) is already obtained for low-quality error observations and limited numbers of test cases. The influence of the number of test cases is of primary importance for continuous (embedded) processing applications, where only limited observation horizons can be maintained.

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On the Accuracy of Spectrum-based Fault Localization

Debugging consumes significant time and effort in any major software development project. Moreover, even after the root cause of a bug is identified, fixing the bug is non-trivial. Given this situation, automated program repair methods are of value. In this paper, we present an automated repair method based on symbolic execution, constraint solving and program synthesis. In our approach, the requirement on the repaired code to pass a given set of tests is formulated as a constraint. Such a constraint is then solved by iterating over a layered space of repair expressions, layered by the complexity of the repair code. We compare our method with recently proposed genetic programming based repair on SIR programs with seeded bugs, as well as fragments of GNU Coreutils with real bugs. On these subjects, our approach reports a higher success-rate than genetic programming based repair, and produces a repair faster.

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SemFix: program repair via semantic analysis

Efficient application scheduling algorithms are important for obtaining high performance in heterogeneous computing systems. In this paper, we present a novel list-based scheduling algorithm called Predict Earliest Finish Time (PEFT) for heterogeneous computing systems. The algorithm has the same time complexity as the state-of-the-art algorithm for the same purpose, that is, O(v2.p) for v tasks and p processors, but offers significant makespan improvements by introducing a look-ahead feature without increasing the time complexity associated with computation of an optimistic cost table (OCT). The calculated value is an optimistic cost because processor availability is not considered in the computation. Our algorithm is only based on an OCT that is used to rank tasks and for processor selection. The analysis and experiments based on randomly generated graphs with various characteristics and graphs of real-world applications show that the PEFT algorithm outperforms the state-of-the-art list-based algorithms for heterogeneous systems in terms of schedule length ratio, efficiency, and frequency of best results.

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List Scheduling Algorithm for Heterogeneous Systems by an Optimistic Cost Table

Automated diagnosis of software faults can improve the efficiency of the debugging process, and is therefore an important technique for the development of dependable software. In this paper we study different similarity coefficients that are applied in the context of a program spectral approach to software fault localization (single programming mistakes). The coefficients studied are taken from the systems diagnosis/automated debugging tools Pinpoint, Tarantula, and AMPLE, and from the molecular biology domain (the Ochiai coefficient). We evaluate these coefficients on the Siemens Suite of benchmark faults, and assess their effectiveness in terms of the position of the actual fault in the probability ranking of fault candidates produced by the diagnosis technique. Our experiments indicate that the Ochiai coefficient consistently outperforms the coefficients currently used by the tools mentioned. In terms of the amount of code that needs to be inspected, this coefficient improves 5% on average over the next best technique, and up to 30% in specific cases

An Evaluation of Similarity Coefficients for Software Fault Localization

Recently (Proc. ACM Int. Conf. on Supercomput., 1999), we presented two very low-cost approaches to compile-time list scheduling where the tasks' priorities are computed statically or dynamically. For homogeneous systems, these two algorithms, called FCP (Fast Critical Path) and FLB (Fast Load Balancing), respectively, have been shown to yield a performance equivalent to other much more costly algorithms, such as MCP and ETF (Earliest Task First). In this paper, we present modified versions of FCP and FLB targeted at heterogeneous systems. We show that the modified versions yield a good overall performance, which is generally comparable to algorithms specifically designed for heterogeneous systems, such as HEFT (Heterogeneous Earliest Finish Time) or ERT (which are versions of MCP and ETF, respectively, using the task's completion time as the task priority). There are a few cases, mainly for irregular problems and large processor speed variance, where FCP's and FLB's performances drop to 32% and 63%, respectively. Considering the good overall performance and their very low cost, however, FCP and FLB are interesting options for scheduling very large problems on heterogeneous systems.

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Fast and effective task scheduling in heterogeneous systems

A relatively new trend in parallel programming scheduling is the so-called mixed task and data scheduling. It has been shown that mixing task and data parallelism to solve large computational applications often yields better speedups compared to either applying more task parallelism or pure data parallelism. In this paper we present a new compile-time heuristic, named critical path and allocation (CPA), for scheduling data-parallel task graphs. Designed to have a very low cost, its complexity is much lower compared to existing approaches, such as TSAS, TwoL or CPR, by one order of magnitude or even more. Experimental results based on graphs derived from real problems as well as synthetic graphs, show that the performance loss of CPA relative to the above algorithms does not exceed 50%. These results are also confirmed by performance measurements of two real applications (i.e., complex matrix multiplication and Strassen matrix multiplication) running on a cluster of workstations.

A low-cost approach towards mixed task and data parallel scheduling

It is well-known that mixing task and data parallelism to solve large computational applications often yields better speedups compared to either applying pure task parallelism or pure data parallelism. Typically, the applications are modeled in terms of a dependence graph of coarse-grain data-parallel tasks, called a data-parallel task graph. In this paper we present a new compile-time heuristic, named Critical Path Reduction (CPR), for scheduling data-parallel task graphs. Experimental results based on graphs derived from real problems as well as synthetic graphs, show that CPR achieves higher speedup compared to other well-known existing scheduling algorithms, at the expense of some higher cost. These results are also confirmed by performance measurements of two real applications (i.e., complex matrix multiplication and Strassen matrix multiplication) running on a cluster of workstations.

A.J.C. van Gemund

Papers

On the Accuracy of Spectrum-based Fault Localization

An Evaluation of Similarity Coefficients for Software Fault Localization

Fast and effective task scheduling in heterogeneous systems

A low-cost approach towards mixed task and data parallel scheduling

CPR: mixed task and data parallel scheduling for distributed systems