Static mapping is the assignment of parallel processes to the processing elements (PEs) of a parallel system, where the assignment does not change during the application's lifetime. In our scenario we model an application's computations and their dependencies by an application graph. This graph is first partitioned into (nearly) equally sized blocks. These blocks need to communicate at block boundaries. To assign the processes to PEs, our goal is to compute a communication-efficient bijective mapping between the blocks and the PEs. This approach of partitioning followed by bijective mapping has many degrees of freedom. Thus, users and developers of parallel applications need to know more about which choices work for which application graphs and which parallel architectures. To this end, we not only develop new mapping algorithms (derived from known greedy methods). We also perform extensive experiments involving different classes of application graphs (meshes and complex networks), architectures of parallel computers (grids and tori), as well as different partitioners and mapping algorithms. Surprisingly, the quality of the partitions, unless very poor, has little influence on the quality of the mapping. More importantly, one of our new mapping algorithms always yields the best results in terms of the quality measure maximum congestion when the application graphs are complex networks. In case of meshes as application graphs, this mapping algorithm always leads in terms of maximum congestion AND maximum dilation, another common quality measure.
Many metaheuristics have been used to solve the mapping problem. U c ar al @cite_9 implement a large variety of methods within a clustering approach, among them genetic algorithms, simulated annealing, tabu search, and particle swarm optimization. The authors require, however, that the processor graph is homogeneous, @math depends only on whether @math or not. Our approach is more general than theirs in that we allow @math to take different values for @math (see Equation ).
@cite_9
2132589243 2025397485 2147715498 1529628103
Mining patterns in graphs has become an important issue in real applications, such as bioinformatics and web mining. We address a graph clustering problem where a cluster is a set of densely connected nodes, under a practical setting that 1) the input is multiple graphs which share a set of nodes but have different edges and 2) a true cluster cannot be found in all given graphs. For this problem, we propose a probabilistic generative model and a robust learning scheme based on variational Bayesian estimation. A key feature of our probabilistic framework is that not only nodes but also given graphs can be clustered at the same time, allowing our model to capture clusters found in only part of all given graphs. We empirically evaluated the effectiveness of the proposed framework on not only a variety of synthetic graphs but also real gene networks, demonstrating that our proposed approach can improve the clustering performance of competing methods in both synthetic and real data. Mixed-machine heterogeneous computing (HC) environments utilize a distributed suite of different high-performance machines, interconnected with high-speed links, to perform different computationally intensive applications that have diverse computational requirements. HC environments are well suited to meet the computational demands of large, diverse groups of tasks. The problem of optimally mapping (defined as matching and scheduling) these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete, requiring the development of heuristic techniques. Selecting the best heuristic to use in a given environment, however, remains a difficult problem, because comparisons are often clouded by different underlying assumptions in the original study of each heuristic. Therefore, a collection of 11 heuristics from the literature has been selected, adapted, implemented, and analyzed under one set of common assumptions. It is assumed that the heuristics derive a mapping statically (i.e., off-line). It is also assumed that a metatask (i.e., a set of independent, noncommunicating tasks) is being mapped and that the goal is to minimize the total execution time of the metatask. The 11 heuristics examined are Opportunistic Load Balancing, Minimum Execution Time, Minimum Completion Time, Min?min, Max?min, Duplex, Genetic Algorithm, Simulated Annealing, Genetic Simulated Annealing, Tabu, and A*. This study provides one even basis for comparison and insights into circumstances where one technique will out-perform another. The evaluation procedure is specified, the heuristics are defined, and then comparison results are discussed. It is shown that for the cases studied here, the relatively simple Min?min heuristic performs well in comparison to the other techniques. Heterogeneous computing (HC) environments composed of interconnected machines with varied computational capabilities are well suited to meet the computational demands of large, diverse groups of tasks. One aspect of resource allocation in HC environments is matching tasks with machines and scheduling task execution on the assigned machines. We will refer to this matching and scheduling process as mapping. The problem of mapping these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete. Therefore, the development of heuristic techniques to find near-optimal solutions is required. In the HC environment investigated, tasks have deadlines, priorities, multiple versions, and may be composed of communicating subtasks. The best static (off-line) techniques from some previous studies are adapted and applied to this mapping problem: a genetic algorithm (GA), a GENITOR-style algorithm, and a two phase greedy technique based on the concept of Min-min heuristics. Simulation studies compare the performance of these heuristics in several overloaded scenarios, i.e., not all tasks can be executed by their deadlines. The performance measure used is the sum of weighted priorities of tasks that completed before their deadline, adjusted based on the version of the task used. It is shown that for the cases studied here, the GENITOR technique finds the best results, but the faster two phase greedy approach also performs very well. A new heuristic procedure for the transportation problem with exclusionary side constraints is developed and implemented. Tabu search, a meta-heuristic method, is used to guide the search to follow a path selectively to prevent from being trapped at local optimal solutions in order to find a global optimal or near global optimal solution. The simplex method on a graph is employed to lead the search from one solution to an adjacent solution in order to take advantage of the underlying network structure of the problem. In the procedure, net changes in cost and in infeasibility are used to measure the attractiveness of a move, and strategic oscillation is used to implement the intensification and diversification functions. A computational experiment was conducted to test the performance of the heuristic procedure and substantial computational results are reported. These results show that the new heuristic procedure finds very good quality solutions and outperforms an existing heuristic procedure in terms of both solution quality and CPU time.