Browsing by Subject "Recursive bipartitioning"
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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 Improving performance of sparse matrix dense matrix multiplication on large-scale parallel systems(Elsevier BV, 2016) Acer, S.; Selvitopi, O.; Aykanat, CevdetWe propose a comprehensive and generic framework to minimize multiple and different volume-based communication cost metrics for sparse matrix dense matrix multiplication (SpMM). SpMM is an important kernel that finds application in computational linear algebra and big data analytics. On distributed memory systems, this kernel is usually characterized with its high communication volume requirements. Our approach targets irregularly sparse matrices and is based on both graph and hypergraph partitioning models that rely on the widely adopted recursive bipartitioning paradigm. The proposed models are lightweight, portable (can be realized using any graph and hypergraph partitioning tool) and can simultaneously optimize different cost metrics besides total volume, such as maximum send/receive volume, maximum sum of send and receive volumes, etc., in a single partitioning phase. They allow one to define and optimize as many custom volume-based metrics as desired through a flexible formulation. The experiments on a wide range of about thousand matrices show that the proposed models drastically reduce the maximum communication volume compared to the standard partitioning models that only address the minimization of total volume. The improvements obtained on volume-based partition quality metrics using our models are validated with parallel SpMM as well as parallel multi-source BFS experiments on two large-scale systems. For parallel SpMM, compared to the standard partitioning models, our graph and hypergraph partitioning models respectively achieve reductions of 14% and 22% in runtime, on average. Compared to the state-of-the-art partitioner UMPa, our graph model is overall 14.5 � faster and achieves an average improvement of 19% in the partition quality on instances that are bounded by maximum volume. For parallel BFS, we show on graphs with more than a billion edges that the scalability can significantly be improved with our models compared to a recently proposed two-dimensional partitioning model.Item Open Access Optimizing nonzero-based sparse matrix partitioning models via reducing latency(Academic Press, 2018) Acer, S.; Selvitopi, O.; Aykanat, CevdetFor the parallelization of sparse matrix-vector multiplication (SpMV) on distributed memory systems, nonzero-based fine-grain and medium-grain partitioning models attain the lowest communication volume and computational imbalance among all partitioning models. This usually comes, however, at the expense of high message count, i.e., high latency overhead. This work addresses this shortcoming by proposing new fine-grain and medium-grain models that are able to minimize communication volume and message count in a single partitioning phase. The new models utilize message nets in order to encapsulate the minimization of total message count. We further fine-tune these models by proposing delayed addition and thresholding for message nets in order to establish a trade-off between the conflicting objectives of minimizing communication volume and message count. The experiments on an extensive dataset of nearly one thousand matrices show that the proposed models improve the total message count of the original nonzero-based models by up to 27% on the average, which is reflected on the parallel runtime of SpMV as an average reduction of 15% on 512 processors.Item Open Access Partitioning models for general medium-grain parallel sparse tensor decomposition(IEEE, 2021) Karsavuran, M. Ozan; Acer, S.; Aykanat, CevdetThe 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.Item Open Access A recursive bipartitioning algorithm for permuting sparse square matrices into block diagonal form with overlap(Society for Industrial and Applied Mathematics, 2013) Acer, S.; Kayaaslan, E.; Aykanat, CevdetWe investigate the problem of symmetrically permuting a square sparse matrix into a block diagonal form with overlap. This permutation problem arises in the parallelization of an explicit formulation of the multiplicative Schwarz preconditioner and a more recent block overlapping banded linear solver as well as its application to general sparse linear systems. In order to formulate this permutation problem as a graph theoretical problem, we define a constrained version of the multiway graph partitioning by vertex separator (GPVS) problem, which is referred to as the ordered GPVS (oGPVS) problem. However, existing graph partitioning tools are unable to solve the oGPVS problem. So, we also show how the recursive bipartitioning framework can be utilized for solving the oGPVS problem. For this purpose, we propose a left-to-right bipartitioning approach together with a novel vertex fixation scheme so that existing 2-way GPVS tools that support fixed vertices can be effectively and efficiently utilized in the recursive bipartitioning framework. Experimental results on a wide range of matrices confirm the validity of the proposed approach. © 2013 Society for Industrial and Applied Mathematics.Item Open Access Recursive bipartitioning models for performance improvement in sparse matrix computations(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 Hypergraph Bipartitioning Framework for Reducing Bandwidth and Latency Costs Simultaneously(IEEE Computer Society, 2017) Selvitopi, O.; Acer, S.; Aykanat, CevdetIntelligent 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.Item Open Access Reduce operations: send volume balancing while minimizing latency(IEEE, 2020) Karsavuran, M. Ozan; Acer, S.; Aykanat, CevdetCommunication 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.Item Open Access Reducing communication overhead in sparse matrix and tensor computations(2020-08) Karsavuran, Mustafa OzanEncapsulating 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.Item Open Access Replicated partitioning for undirected hypergraphs(Academic Press, 2012) Selvitopi, R. O.; Turk, A.; Aykanat, CevdetHypergraph partitioning (HP) and replication are diverse but powerful tools that are traditionally applied separately to minimize the costs of parallel and sequential systems that access related data or process related tasks. When combined together, these two techniques have the potential of achieving significant improvements in performance of many applications. In this study, we provide an approach involving a tool that simultaneously performs replication and partitioning of the vertices of an undirected hypergraph whose vertices represent data and nets represent task dependencies among these data. In this approach, we propose an iterative-improvement-based replicated bipartitioning heuristic, which is capable of move, replication, and unreplication of vertices. In order to utilize our replicated bipartitioning heuristic in a recursive bipartitioning framework, we also propose appropriate cut-net removal, cut-net splitting, and pin selection algorithms to correctly encapsulate the two most commonly used cutsize metrics. We embed our replicated bipartitioning scheme into the state-of-the-art multilevel HP tool PaToH to provide an effective and efficient replicated HP tool, rpPaToH. The performance of the techniques proposed and the tools developed is tested over the undirected hypergraphs that model the communication costs of parallel query processing in information retrieval systems. Our experimental analysis indicates that the proposed technique provides significant improvements in the quality of the partitions, especially under low replication ratios. © 2012 Elsevier Inc. All rights reserved.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, CevdetLatency 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.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.