Browsing by Author "Acer, Seher"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item Open Access Addressing volume and latency overheads in 1d-parallel sparse matrix-vector multiplication(Springer, 2017-08-09) Acer, Seher; Selvitopi, Oğuz; Aykanat, CevdetThe 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.Item Open Access A hypergraph partitioning model for profile minimization(Society for Industrial and Applied Mathematics Publications, 2019) Acer, Seher; Kayaaslan, E.; Aykanat, CevdetIn this paper, the aim is to symmetrically permute the rows and columns of a given sparse symmetric matrix so that the profile of the permuted matrix is minimized. We formulate this permutation problem by first defining the m-way ordered hypergraph partitioning (moHP) problem and then showing the correspondence between profile minimization and moHP problems. For solving the moHP problem, we propose a recursive-bipartitioning-based hypergraph partitioning algorithm, which we refer to as the moHP algorithm. This algorithm achieves a linear part ordering via left-toright bipartitioning. In this algorithm, we utilize fixed vertices and two novel cut-net manipulation techniques in order to address the minimization objective of the moHP problem. We show the correctness of the moHP algorithm and describe how the existing partitioning tools can be utilized for its implementation. Experimental results on an extensive set of matrices show that the moHP algorithm obtains a smaller profile than the state-of-the-art profile reduction algorithms, which then results in considerable improvements in the factorization runtime in a direct solver.Item Open Access Recursive bipartitioning models for performance improvement in sparse matrix computations(Bilkent University, 2017-08) Acer, SeherSparse 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.Item Open Access A recursive graph bipartitioning algorithm by vertex separators with fixed vertices for permuting sparse matrices into block diagonal form with overlap(Bilkent University, 2011) Acer, SeherSolving sparse system of linear equations Ax=b using preconditioners can be effi- ciently parallelized using graph partitioning tools. In this thesis, we investigate the problem of permuting a sparse matrix into a block diagonal form with overlap which is to be used in the parallelization of the multiplicative schwarz preconditioner. A matrix is said to be in block diagonal form with overlap if the diagonal blocks may overlap. In order to formulate this permutation problem as a graph-theoretical problem, we introduce a restricted version of the graph partitioning by vertex separator problem (GPVS), where the objective is to find a vertex partition whose parts are only connected by a vertex separator. The modified problem, we refer as ordered GPVS problem (oGPVS), is restricted such that the parts should exhibit an ordered form where the consecutive parts can only be connected by a separator. The existing graph partitioning tools are unable to solve the oGPVS problem. Thus, we present a recursive graph bipartitioning algorithm by vertex separators together with a novel vertex fixation scheme so that a GPVS tool supporting fixed vertices can effectively and efficiently be utilized. We also theoretically verified the correctness of the proposed approach devising a necessary and sufficient condition to the feasibility of a oGPVS solution. Experimental results on a wide range of matrices confirm the validity of the proposed approach.Item Open Access Simultaneous computational and data load balancing in distributed-memory setting(SIAM, 2022) Çeliktuğ, Mestan Fırat; Karsavuran, M. Ozan; Acer, Seher; Aykanat, Cevdet; Sterck, Hans DeSeveral successful partitioning models and methods have been proposed and used for computational load balancing of irregularly sparse applications in a distributed-memory setting. However, the literature lacks partitioning models and methods that encode both computational and data load balancing. In this article, we try to close this gap in the literature by proposing two hypergraph partitioning (HP) models which simultaneously encode computational and data load balancing. Both models utilize a two-constraint formulation, where the first constraint encodes the computational loads and the second constraint encodes the data loads. In the first model, we introduce explicit data vertices for encoding data load and we replicate those data vertices at each recursive bipartitioning (RB) step for encoding data replication. In the second model, we introduce a data weight distribution scheme for encoding data load and we update those weights at each RB step. The nice property of both proposed models is that they do not necessitate developing a new partitioner from scratch. Both models can easily be implemented by invoking any HP tool that supports multiconstraint partitioning as a two-way partitioner at each RB step. The validity of the proposed models are tested on two widely used irregularly sparse applications: parallel mesh simulations and parallel sparse matrix sparse matrix multiplication. Both proposed models achieve significant improvement over a baseline model.