### Browsing by Subject "Communication cost"

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Item Open Access Addressing volume and latency overheads in 1d-parallel sparse matrix-vector multiplication(Springer, 2017-08-09) Acer, Seher; Selvitopi, Oğuz; Aykanat, CevdetShow more The scalability of sparse matrix-vector multiplication (SpMV) on distributed memory systems depends on multiple factors that involve different communication cost metrics. The irregular sparsity pattern of the coefficient matrix manifests itself as high bandwidth (total and/or maximum volume) and/or high latency (total and/or maximum message count) overhead. In this work, we propose a hypergraph partitioning model which combines two earlier models for one-dimensional partitioning, one addressing total and maximum volume, and the other one addressing total volume and total message count. Our model relies on the recursive bipartitioning paradigm and simultaneously addresses three cost metrics in a single partitioning phase in order to reduce volume and latency overheads. We demonstrate the validity of our model on a large dataset that contains more than 300 matrices. The results indicate that compared to the earlier models, our model significantly improves the scalability of SpMV. © 2017, Springer International Publishing AG.Show more Item Open Access Cartesian partitioning models for 2D and 3D parallel SpGEMM algorithms(IEEE, 2020) Demirci, Gündüz Vehbi; Aykanat, CevdetShow more The focus is distributed-memory parallelization of sparse-general-matrix-multiplication (SpGEMM). Parallel SpGEMM algorithms are classified under one-dimensional (1D), 2D, and 3D categories denoting the number of dimensions by which the 3D sparse workcube representing the iteration space of SpGEMM is partitioned. Recently proposed successful 2D- and 3D-parallel SpGEMM algorithms benefit from upper bounds on communication overheads enforced by 2D and 3D cartesian partitioning of the workcube on 2D and 3D virtual processor grids, respectively. However, these methods are based on random cartesian partitioning and do not utilize sparsity patterns of SpGEMM instances for reducing the communication overheads. We propose hypergraph models for 2D and 3D cartesian partitioning of the workcube for further reducing the communication overheads of these 2D- and 3D- parallel SpGEMM algorithms. The proposed models utilize two- and three-phase partitioning that exploit multi-constraint hypergraph partitioning formulations. Extensive experimentation performed on 20 SpGEMM instances by using upto 900 processors demonstrate that proposed partitioning models significantly improve the scalability of 2D and 3D algorithms. For example, in 2D-parallel SpGEMM algorithm on 900 processors, the proposed partitioning model respectively achieves 85 and 42 percent decrease in total volume and total number of messages, leading to 1.63 times higher speedup compared to random partitioning, on average.Show more Item Open Access Partitioning models for general medium-grain parallel sparse tensor decomposition(IEEE, 2021) Karsavuran, M. Ozan; Acer, S.; Aykanat, CevdetShow more The focus of this article is efficient parallelization of the canonical polyadic decomposition algorithm utilizing the alternating least squares method for sparse tensors on distributed-memory architectures. We propose a hypergraph model for general medium-grain partitioning which does not enforce any topological constraint on the partitioning. The proposed model is based on splitting the given tensor into nonzero-disjoint component tensors. Then a mode-dependent coarse-grain hypergraph is constructed for each component tensor. A net amalgamation operation is proposed to form a composite medium-grain hypergraph from these mode-dependent coarse-grain hypergraphs to correctly encapsulate the minimization of the communication volume. We propose a heuristic which splits the nonzeros of dense slices to obtain sparse slices in component tensors. So we partially attain slice coherency at (sub)slice level since partitioning is performed on (sub)slices instead of individual nonzeros. We also utilize the well-known recursive-bipartitioning framework to improve the quality of the splitting heuristic. Finally, we propose a medium-grain tripartite graph model with the aim of a faster partitioning at the expense of increasing the total communication volume. Parallel experiments conducted on 10 real-world tensors on up to 1024 processors confirm the validity of the proposed hypergraph and graph models.Show more Item Open Access Partitioning models for scaling parallel sparse matrix-matrix multiplication(Association for Computing Machinery, 2018) Akbudak, Kadir; Selvitopi, Oğuz; Aykanat, CevdetShow more We investigate outer-product--parallel, inner-product--parallel, and row-by-row-product--parallel formulations of sparse matrix-matrix multiplication (SpGEMM) on distributed memory architectures. For each of these three formulations, we propose a hypergraph model and a bipartite graph model for distributing SpGEMM computations based on one-dimensional (1D) partitioning of input matrices. We also propose a communication hypergraph model for each formulation for distributing communication operations. The computational graph and hypergraph models adopted in the first phase aim at minimizing the total message volume and balancing the computational loads of processors, whereas the communication hypergraph models adopted in the second phase aim at minimizing the total message count and balancing the message volume loads of processors. That is, the computational partitioning models reduce the bandwidth cost and the communication hypergraph models reduce the latency cost. Our extensive parallel experiments on up to 2048 processors for a wide range of realistic SpGEMM instances show that although the outer-product--parallel formulation scales better, the row-by-row-product--parallel formulation is more viable due to its significantly lower partitioning overhead and competitive scalability. For computational partitioning models, our experimental findings indicate that the proposed bipartite graph models are attractive alternatives to their hypergraph counterparts because of their lower partitioning overhead. Finally, we show that by reducing the latency cost besides the bandwidth cost through using the communication hypergraph models, the parallel SpGEMM time can be further improved up to 32%.Show more Item Open Access Recursive bipartitioning models for performance improvement in sparse matrix computations(Bilkent University, 2017-08) Acer, SeherShow more Sparse matrix computations are among the most important building blocks of linear algebra and arise in many scienti c and engineering problems. Depending on the problem type, these computations may be in the form of sparse matrix dense matrix multiplication (SpMM), sparse matrix vector multiplication (SpMV), or factorization of a sparse symmetric matrix. For both SpMM and SpMV performed on distributed-memory architectures, the associated data and task partitions among processors a ect the parallel performance in a great extent, especially for the sparse matrices with an irregular sparsity pattern. Parallel SpMM is characterized by high volumes of data communicated among processors, whereas both the volume and number of messages are important for parallel SpMV. For the factorization performed in envelope methods, the envelope size (i.e., pro le) is an important factor which determines the performance. For improving the performance in each of these sparse matrix computations, we propose graph/hypergraph partitioning models that exploit the advantages provided by the recursive bipartitioning (RB) paradigm in order to meet the speci c needs of the respective computation. In the models proposed for SpMM and SpMV, we utilize the RB process to enable targeting multiple volume-based communication cost metrics and the combination of volume- and number-based communication cost metrics in their partitioning objectives, respectively. In the model proposed for the factorization in envelope methods, the input matrix is reordered by utilizing the RB process in which two new quality metrics relating to pro le minimization are de ned and maintained. The experimantal results show that the proposed RB-based approach outperforms the state-of-the-art for each mentioned computation.Show more Item Open Access A Recursive Hypergraph Bipartitioning Framework for Reducing Bandwidth and Latency Costs Simultaneously(IEEE Computer Society, 2017) Selvitopi, O.; Acer, S.; Aykanat, CevdetShow more Intelligent partitioning models are commonly used for efficient parallelization of irregular applications on distributed systems. These models usually aim to minimize a single communication cost metric, which is either related to communication volume or message count. However, both volume- and message-related metrics should be taken into account during partitioning for a more efficient parallelization. There are only a few works that consider both of them and they usually address each in separate phases of a two-phase approach. In this work, we propose a recursive hypergraph bipartitioning framework that reduces the total volume and total message count in a single phase. In this framework, the standard hypergraph models, nets of which already capture the bandwidth cost, are augmented with message nets. The message nets encode the message count so that minimizing conventional cutsize captures the minimization of bandwidth and latency costs together. Our model provides a more accurate representation of the overall communication cost by incorporating both the bandwidth and the latency components into the partitioning objective. The use of the widely-adopted successful recursive bipartitioning framework provides the flexibility of using any existing hypergraph partitioner. The experiments on instances from different domains show that our model on the average achieves up to 52 percent reduction in total message count and hence results in 29 percent reduction in parallel running time compared to the model that considers only the total volume. © 2016 IEEE.Show more Item Open Access Reduce operations: send volume balancing while minimizing latency(IEEE, 2020) Karsavuran, M. Ozan; Acer, S.; Aykanat, CevdetShow more Communication hypergraph model was proposed in a two-phase setting for encapsulating multiple communication cost metrics (bandwidth and latency), which are proven to be important in parallelizing irregular applications. In the first phase, computational-task-to-processor assignment is performed with the objective of minimizing total volume while maintaining computational load balance. In the second phase, communication-task-to-processor assignment is performed with the objective of minimizing total number of messages while maintaining communication-volume balance. The reduce-communication hypergraph model suffers from failing to correctly encapsulate send-volume balancing. We propose a novel vertex weighting scheme that enables part weights to correctly encode send-volume loads of processors for send-volume balancing. The model also suffers from increasing the total communication volume during partitioning. To decrease this increase, we propose a method that utilizes the recursive bipartitioning framework and refines each bipartition by vertex swaps. For performance evaluation, we consider column-parallel SpMV, which is one of the most widely known applications in which the reduce-task assignment problem arises. Extensive experiments on 313 matrices show that, compared to the existing model, the proposed models achieve considerable improvements in all communication cost metrics. These improvements lead to an average decrease of 30 percent in parallel SpMV time on 512 processors for 70 matrices with high irregularity.Show more Item Open Access Reducing communication overhead in sparse matrix and tensor computations(Bilkent University, 2020-08) Karsavuran, Mustafa OzanShow more Encapsulating multiple communication cost metrics, i.e., bandwidth and latency, is proven to be important in reducing communication overhead in the parallelization of sparse and irregular applications. Communication hypergraph model was proposed in a two-phase setting for encapsulating multiple communication cost metrics. The reduce-communication hypergraph model suﬀers from failing to correctly encapsulate send-volume balancing. We propose a novel vertex weighting scheme that enables part weights to correctly encode send-volume loads of processors for send-volume balancing. The model also suﬀers from increasing the total communication volume during partitioning. To decrease this increase, we propose a method that utilizes the recursive bipartitioning (RB) paradigm and reﬁnes each bipartition by vertex swaps. For performance evaluation, we consider column-parallel SpMV, which is one of the most widely known applications in which the reduce-task assignment problem arises. Extensive experiments on 313 matrices show that, compared to the existing model, the proposed models achieve considerable improvements in all communication cost metrics. These improvements lead to an average decrease of 30 percent in parallel SpMV time on 512 processors for 70 matrices with high irregularity. We further enhance the reduce-communication hypergraph model so that it also encapsulates the minimization of the maximum number of messages sent by a processor. For this purpose, we propose a novel cutsize metric which we realize using RB paradigm while partitioning the reduce-communication hypergraph. We also introduce a new type of net for the communication hypergraph which models decreasing the increase in the total communication volume directly with the partitioning objective. Experiments on 300 matrices show that the proposed models achieve considerable improvements in communication cost metrics which lead to better column-parallel SpMM time on 1024 processors. We propose a hypergraph model for general medium-grain sparse tensor partitioning which does not enforce any topological constraint on the partitioning. The proposed model is based on splitting the given tensor into nonzero-disjoint component tensors. Then a mode-dependent coarse-grain hypergraph is constructed for each component tensor. A net amalgamation operation is proposed to form a composite medium-grain hypergraph from these mode-dependent coarse-grain hypergraphs to correctly encapsulate the minimization of the communication volume. We propose a heuristic which splits the nonzeros of dense slices to obtain sparse slices in component tensors. We also utilize the well-known RB paradigm to improve the quality of the splitting heuristic. We propose a medium-grain tripartite graph model with the aim of a faster partitioning at the expense of increasing the total communication volume. Parallel experiments conducted on 10 real-world tensors on up to 1024 processors conﬁrm the validity of the proposed hypergraph and graph models.Show more Item Open Access Scalable unsupervised ML: Latency hiding in distributed sparse tensor decomposition(IEEE Computer Society, 2022-11-01) Abubaker, Nabil; Karsavuran, M. Ozan; Aykanat, CevdetShow more Latency overhead in distributed-memory parallel CPD-ALS scales with the number of processors, limiting the scalability of computing CPD of large irregularly sparse tensors. This overhead comes in the form of sparse reduce and expand operations performed on factor-matrix rows via point-to-point messages. We propose to hide the latency overhead through embedding all of the point-to-point messages incurred by the sparse reduce and expand into dense collective operations which already exist in the CPD-ALS. The conventional parallel CPD-ALS algorithm is not amenable for embedding so we propose a computation/communication rearrangement to enable the embedding. We embed the sparse expand and reduce into a hypercube-based ALL-REDUCE operation to limit the latency overhead to Oðlog 2KÞ for a K-processor system. The embedding comes with the cost of increased bandwidth overhead due to the multi-hop routing of factor-matrix rows during the embedded-ALL-REDUCE. We propose an embedding scheme that takes advantage of the expand/reduce properties to reduce this overhead. Furthermore, we propose a novel recursive bipartitioning framework that enables simultaneous hypergraph partitioning and subhypergraph-to-subhypercube mapping to achieve subtensor-to-processor assignment with the objective of reducing the bandwidth overhead during the embedded-ALL-REDUCE. We also propose a bin-packing-based algorithm for factor-matrix row to processor assignment aiming at reducing processors’ maximum send and receive volumes during the embedded-ALL-REDUCE. Experiments on up to 4096 processors show that the proposed framework scales significantly better than the state-of-the-art point-to-point method.Show more Item Open Access Voltage island based heterogeneous NoC design through constraint programming(Pergamon Press, 2014) Demiriz, A.; Bagherzadeh, N.; Ozturk, O.Show more This paper discusses heterogeneous Network-on-Chip (NoC) design from a Constraint Programming (CP) perspective and extends the formulation to solving Voltage-Frequency Island (VFI) problem. In general, VFI is a superior design alternative in terms of thermal constraints, power consumption as well as performance considerations. Given a Communication Task Graph (CTG) and subsequent task assignments for cores, cores are allocated to the best possible places on the chip in the first stage to minimize the overall communication cost among cores. We then solve the application scheduling problem to determine the optimum core types from a list of technological alternatives and to minimize the makespan. Moreover, an elegant CP model is proposed to solve VFI problem by mapping and grouping cores at the same time with scheduling the computation tasks as a limited capacity resource allocation model. The paper reports results based on real benchmark datasets from the literature.Show more