Browsing by Subject "Parallel processing"
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Item Open Access A stochastic programming approach to surgery scheduling under parallel processing principle(Elsevier Ltd, 2023-11-06) Çelik, Batuhan; Gül, Serhat; Çelik, MelihParallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to IRs at the second stage of the model. We show that an optimal myopic policy can be used for IR assignment decisions due to the special structure of the model. We minimize the expected total cost of patient waiting time, OR idle time and IR idle time in the objective function. We enhance the model formulation using bounds on variables and symmetry-breaking constraints. We implement a novel progressive hedging algorithm by proposing a penalty update method and a variable fixing mechanism. Based on real data of a large academic hospital, we compare our solution approach with several scheduling heuristics from the literature. We assess the additional benefits and costs associated with the implementation of parallel processing using near-optimal schedules. We examine how the benefits are inflated by increasing the number of IRs. Finally, we estimate the value of stochastic solution to underline the importance of considering uncertainty in durations. © 2022 Elsevier LtdItem Open Access Foreword: 1st International Workshop on High Performance Computing for Big Data(IEEE, 2014-09) Kaya, Kamer; Gedik, Buğra; Çatalyürek, Ümit V.The 1st International Workshop on High Performance Computing for Big Data (HPC4BD) is held on September 10, 2014 in concordance with 43rd International Conference on Parallel Processing (ICPP-2014). The workshop aimed to bring high performance computing (HPC) experts and experts from various application domains together to discuss their Big Data problems. There were four works accepted to be presented in this year's workshop. This foreword presents a summary of the them. © 2014 IEEE.Item Open Access Hypergraph models for sparse matrix partitioning and reordering(1999-11) Çatalyürek, Ümit VeyselGraphs have been widely used to represent sparse matrices for various scientific applications including one-dimensional (ID) decomposition of sparse matrices for parallel sparse-matrix vector multiplication (SpMxV) and sparse matrix reordering for low fill factorization. The standard graph-partitioning based ID decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel SpMxV. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model on ID decomposition. The proposed models reduce the ID decomposition problem to the well-known hypergraph partitioning problem. In the literature, there is a lack of 2D decomposition heuristic which directly minimizes the communication requirements for parallel SpMxV computations. Three novel hypergraph models are introduced for 2D decomposition of sparse matrices for minimizing the communication volume requirement. The first hypergraph model is proposed for fine-grain 2D decomposition of the sparse matrices for parallel SpMxV. The second hypergraph model for 2D decomposition is proposed to produce jagged-like decomposition of the sparse matrix. The checkerboard decomposition based parallel matrix-vector multiplication algorithms are widely encountered in the literature. However, only the load balancing problem is addressed in those works. Here, we propose a new hypergraph model which aims the minimization of communication volume while maintaining the load balance among the processors for checkerboard decomposition, as the third model for 2D decomposition. The proposed model reduces the decomposition problem to the multi-constraint hypergraph partitioning problem. The notion of multi-constraint partitioning has recently become popular in graph partitioning. We applied the multi-constraint partitioning to the hypergraph partitioning problem for solving checkerboard partitioning. Graph partitioning by vertex separator (GPVS) is widely used for nested dissection based low fill ordering of sparse matrices for direct solution of linear systems. In this work, we also show that the GPVS problem can be formulated as hypergraph partitioning. We exploit this finding to develop a novel hypergraph partitioning-based nested dissection ordering. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In terms of communication volume, the proposed hypergraph models produce 30% and 59% better decompositions than the graph model in ID and 2D decompositions of sparse matrices for parallel SpMxV computations, respectively. The proposed hypergraph partitioning-based nested dissection produces 25% to 45% better orderings than the widely used multiple mimirnum degree ordering in the ordering of various test matrices arising from different applications.Item Open Access Spatial subdivision for parallel ray casting/tracing(1995) İşler, VeysiRay casting/tracing has been extensively studied for a long time, since it is an elegant way of producing realistic images. However, it is a computationally intensive algorithm. In this study, a taxonomy of parallel ray casting/tracing algorithms is presented cind the primary parallel ray casting/tracing systems are discussed and criticized. This work mainly focuses on the utilization of spatial subdivision technique for ray casting/tracing on a distributed-memory MIMD parallel computer. In this research, the reason for the use of parallel computers is not only the processing power but also the large memory space provided by them. The spatial subdivision technique has been adapted to parallel ray casting/tracing to decompose a three-dimensional complex scene that may not fit into the local memory of a single processor. The decomposition method achieves an even distribution of scene objects while allowing to exploit graphical coherence. Additionally, the decomposition method produces three-dimensional volumes which are mapped inexpensively to the processors so that the objects within adjacent volumes are stored in the local memories of close processors to decrease interprocessor communication cost. Then, the developed decomposition and mapping methods have been parallelized efficiently to reduce the preprocessing overhead. Finally, a splitting plane concept (called “jaggy splitting plane”) has been proposed to accomplish full utilization of the memory space of processors. Jaggy splitting plane avoids the shared objects which are the major sources of inefficient utilization of both memory and processing power. The proposed parallel algorithms have been implemented on the Intel iPSC/2 hypercube multicomputer (distributed-memory MIMD).