Browsing by Author "Kayaaslan, E."

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Open Access
1.5D parallel sparse matrix-vector multiply
(Society for Industrial and Applied Mathematics, 2018) Kayaaslan, E.; Aykanat, Cevdet; Uçar, B.
There are three common parallel sparse matrix-vector multiply algorithms: 1D row-parallel, 1D column-parallel, and 2D row-column-parallel. The 1D parallel algorithms offer the advantage of having only one communication phase. On the other hand, the 2D parallel algorithm is more scalable, but it suffers from two communication phases. Here, we introduce a novel concept of heterogeneous messages where a heterogeneous message may contain both input-vector entries and partially computed output-vector entries. This concept not only leads to a decreased number of messages but also enables fusing the input- and output-communication phases into a single phase. These findings are exploited to propose a 1.5D parallel sparse matrix-vector multiply algorithm which is called local row-column-parallel. This proposed algorithm requires a constrained fine-grain partitioning in which each fine-grain task is assigned to the processor that contains either its input-vector entry, its output-vector entry, or both. We propose two methods to carry out the constrained fine-grain partitioning. We conduct our experiments on a large set of test matrices to evaluate the partitioning qualities and partitioning times of these proposed 1.5D methods.
Open Access
Document replication strategies for geographically distributed web search engines
(Elsevier Ltd., 2013) Kayaaslan, E.; Cambazoglu, B. B.; Aykanat, Cevdet
Large-scale web search engines are composed of multiple data centers that are geographically distant to each other. Typically, a user query is processed in a data center that is geographically close to the origin of the query, over a replica of the entire web index. Compared to a centralized, single-center search engine, this architecture offers lower query response times as the network latencies between the users and data centers are reduced. However, it does not scale well with increasing index sizes and query traffic volumes because queries are evaluated on the entire web index, which has to be replicated and maintained in all data centers. As a remedy to this scalability problem, we propose a document replication framework in which documents are selectively replicated on data centers based on regional user interests. Within this framework, we propose three different document replication strategies, each optimizing a different objective: reducing the potential search quality loss, the average query response time, or the total query workload of the search system. For all three strategies, we consider two alternative types of capacity constraints on index sizes of data centers. Moreover, we investigate the performance impact of query forwarding and result caching. We evaluate our strategies via detailed simulations, using a large query log and a document collection obtained from the Yahoo! web search engine. (C) 2012 Elsevier Ltd. All rights reserved.
Open Access
Hypergraph partitioning based models and methods for exploiting cache locality in sparse matrix-vector multiplication
(Society for Industrial and Applied Mathematics, 2013-02-27) Akbudak, K.; Kayaaslan, E.; Aykanat, Cevdet
Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate single-and multiple-SpMxV frameworks for exploiting cache locality in SpMxV computations. For the single-SpMxV framework, we propose two cache-size-aware row/column reordering methods based on one-dimensional (1D) and two-dimensional (2D) top-down sparse matrix partitioning. We utilize the column-net hypergraph model for the 1D method and enhance the row-column-net hypergraph model for the 2D method. The primary aim in both of the proposed methods is to maximize the exploitation of temporal locality in accessing input vector entries. The multiple-SpMxV framework depends on splitting a given matrix into a sum of multiple nonzero-disjoint matrices. We propose a cache-size-aware splitting method based on 2D top-down sparse matrix partitioning by utilizing the row-column-net hypergraph model. The aim in this proposed method is to maximize the exploitation of temporal locality in accessing both input-and output-vector entries. We evaluate the validity of our models and methods on a wide range of sparse matrices using both cache-miss simulations and actual runs by using OSKI. Experimental results show that proposed methods and models outperform state-of-the-art schemes. (c)2013 Society for Industrial and Applied Mathematics
Open Access
A hypergraph partitioning model for profile minimization
(Society for Industrial and Applied Mathematics Publications, 2019) Acer, Seher; Kayaaslan, E.; Aykanat, Cevdet
In 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.
Open Access
Hypergraph partitioning-based fill-reducing ordering for symmetric matrices
(Society for Industrial and Applied Mathematics, 2011) Çatalyürek, Ü. V.; Aykanat, Cevdet; Kayaaslan, E.
A typical first step of a direct solver for the lin ear system Mx = b is reordering of the symmetric matrix M to improve execution time and space requirements of the solution process. In this work, we propose a novel nested-dissection-based ordering approach that utilizes hypergraph partitioning. Our approach is based on the formulation of graph partitioning by vertex separator (GPVS) problem as a hypergraph partitioning problem. This new formulation is immune to deficiency of GPVS in a multilevel framework and hence enables better orderings. In matrix terms, our method relies on the existence of a structural factorization of the input M matrix in the form of M = AA T (or M = AD2AT). We show that the partitioning of the row-net hypergraph representation of the rectangular matrix A induces a GPVS of the standard graph representation of matrix M. In the absence of such factorization, we also propose simple, yet effective structural factorization techniques that are based on finding an edge clique cover of the standard graph representation of matrix M, and hence applicable to any arbitrary symmetric matrix M. Our experimental evaluation has shown that the proposed method achieves better ordering in comparison to state-of-the-art graph-based ordering tools even for symmetric matrices where structural M = AAT factorization is not provided as an input. For matrices coming from linear programming problems, our method enables even faster and better orderings. © 2011 Societ y for Industrial and Applied Mathematics.
Open Access
Partitioning hypergraphs in scientific computing applications through vertex separators on graphs
(Society for Industrial and Applied Mathematics, 2012) Kayaaslan, E.; Pinar, A.; Çatalyürek, U.; Aykanat, Cevdet
The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The modeling flexibility of hypergraphs, however, comes at a cost: algorithms on hypergraphs are inherently more complicated than those on graphs, which sometimes translates to nontrivial increases in processing times. Neither the modeling flexibility of hypergraphs nor the runtime efficiency of graph algorithms can be overlooked. Therefore, the new research thrust should be how to cleverly trade off between the two. This work addresses one method for this trade-off by solving the hypergraph partitioning problem by finding vertex separators on graphs. Specifically, we investigate how to solve the hypergraph partitioning problem by seeking a vertex separator on its net intersection graph (NIG), where each net of the hypergraph is represented by a vertex, and two vertices share an edge if their nets have a common vertex. We propose a vertex-weighting scheme to attain good node-balanced hypergraphs, since the NIG model cannot preserve node-balancing information. Vertex-removal and vertex-splitting techniques are described to optimize cut-net and connectivity metrics, respectively, under the recursive bipartitioning paradigm. We also developed implementations of our proposed hypergraph partitioning formulations by adopting and modifying a state-of-the-art graph partitioning by vertex separator tool onmetis. Experiments conducted on a large collection of sparse matrices demonstrate the effectiveness of our proposed techniques. (c) 2012 Society for Industrial and Applied Mathematics.
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, Cevdet
We 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.
Open Access
A term-based inverted index partitioning model for efficient distributed query processing
(Association for Computing Machinery, 2013) Cambazoglu, B. B.; Kayaaslan, E.; Jonassen, S.; Aykanat, Cevdet
In a shared-nothing, distributed text retrieval system, queries are processed over an inverted index that is partitioned among a number of index servers. In practice, the index is either document-based or term-based partitioned. This choice is made depending on the properties of the underlying hardware infrastructure, query traffic distribution, and some performance and availability constraints. In query processing on retrieval systems that adopt a term-based index partitioning strategy, the high communication overhead due to the transfer of large amounts of data from the index servers forms a major performance bottleneck, deteriorating the scalability of the entire distributed retrieval system. In this work, to alleviate this problem, we propose a novel inverted index partitioning model that relies on hypergraph partitioning. In the proposed model, concurrently accessed index entries are assigned to the same index servers, based on the inverted index access patterns extracted from the past query logs. The model aims tominimize the communication overhead that will be incurred by future queries while maintaining the computational load balance among the index servers. We evaluate the performance of the proposed model through extensive experiments using a real-life text collection and a search query sample. Our results show that considerable performance gains can be achieved relative to the term-based index partitioning strategies previously proposed in literature. In most cases, however, the performance remains inferior to that attained by document-based partitioning. © 2013 ACM.