Hypergraph-based data partitioning

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph.D.) -- Bilkent University, 2013Includes bibliographical references leaves 96-103.A hypergraph is a general version of graph where the edges may connect any number of vertices. By this flexibility, hypergraphs has a larger modeling power that may allow accurate formulaion of many problems of combinatorial scientific computing. This thesis discusses the use of hypergraph-based approaches to solve problems that require data partitioning. The thesis is composed of three parts. In the first part, we show how to implement hypergraph partitioning efficiently using recursive graph bipartitioning. The remaining two parts show how to formulate two important data partitioning problems in parallel computing as hypergraph partitioning. The first problem is global inverted index partitioning for parallel query processing and the second one is row-columnwise sparse matrix partitioning for parallel matrix vector multiplication, where both multiplication and sparse matrix partitioning schemes has novelty. In this thesis, we show that hypergraph models achieve partitions with better quality.Kayaaslan, EnverPh.D

Analyzing and enhancing OSKI for sparse matrix-vector multiplication

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 top-down row/column-reordering methods based on 1D and 2D sparse matrix partitioning by utilizing the column-net and enhancing the row-column-net hypergraph models of sparse matrices. The multiple-SpMxV framework depends on splitting a given matrix into a sum of multiple nonzero-disjoint matrices so that the SpMxV operation is performed as a sequence of multiple input- and output-dependent SpMxV operations. For an effective matrix splitting required in this framework, we propose a cache-size-aware top-down approach based on 2D sparse matrix partitioning by utilizing the row-column-net hypergraph model. The primary objective in all of the three methods is to maximize the exploitation of temporal locality. We evaluate the validity of our models and methods on a wide range of sparse matrices by performing actual runs through using OSKI. Experimental results show that proposed methods and models outperform state-of-the-art schemes.Comment: arXiv admin note: substantial text overlap with arXiv:1202.385

Combinatorial reductions between graph partitioning by vertex separator and hypergraph partitioning problems for parallel and scientific computing applications

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 81-85.Colour as an effective design tool influences people’s emotions in interior spaces. Depending on the assumption that colour has an impact on human psychology, this study stresses the need for further studies that comprise colour and emotion association in interior space in order to provide healthier spaces for inhabitants. Emotional reactions to colour in a living room were investigated by using self report measure. Pure red, green and blue were chosen to be investigated as chromatic colours, whereas gray was the achromatic colour used as a control variable. The study was conducted at Bilkent University in Ankara, Turkey. Hundred and eighty people from various ages and academic departments participated in the study. Participants first watched a short video showing an overlook of a 3D model of a living room. Next, they were asked to match the distinct coloured living rooms with facial expressions of six basic emotions that covers anger, disgust, surprise, happiness, fear, sadness and in addition with neutral. The results of the study indicated that the most stated emotions associated for the room with red walls were disgust and happiness, while the least stated emotions were sadness, fear, anger, and surprise. Neutral and happiness were the most stated emotions for the room with green walls and anger, surprise, fear and sadness were the least stated ones. The most stated emotion associated for the room with blue walls was neutral, while the least stated emotions were anger and surprise. Neutral, disgust and sadness were the most stated emotions for the room with gray walls. Gender differences were not found in human emotional reactions to living rooms with different wall colours.Kayaaslan, EnverM.S

partition by quasi-cliques problems

On the minimum edge cover and vertex partition by quasi-cliques problem

Reducing elimination tree height for parallel LU factorization of sparse unsymmetric matrices

International audienceThe elimination tree for unsymmetric matrices is a recent model playing important roles in sparse LU factorization. This tree captures the dependencies between the tasks of some well-known variants of sparse LU factorization. Therefore, the height of the elimination tree corresponds to the critical path length of the task dependency graph in the corresponding parallel LU factorization methods. We investigate the problem of finding minimum height elimination trees to expose a maximum degree of parallelism by minimizing the critical path length. This problem has recently been shown to be NP-complete. Therefore, we propose heuristics, which generalize the most successful approaches used for symmetric matrices to unsymmetric ones. We test the proposed heuristics on a large set of real world matrices and report 28% reduction in the elimination tree heights with respect to a common method, which exploits the state of the art tools used in Cholesky factorization

Semi-two-dimensional partitioning for parallel sparse matrix-vector multiplication

International audienceWe propose a novel sparse matrix partitioning scheme, called semi-two-dimensional (s2D), for efficient paral-lelization of sparse matrix-vector multiply (SpMV) operations on distributed memory systems. In s2D, matrix nonzeros are more flexibly distributed among processors than one dimensional (rowwise or columnwise) partitioning schemes. Yet, there is a constraint which renders s2D less flexible than two-dimensional (nonzero based) partitioning schemes. The constraint is enforced to confine all communication operations in a single phase, as in 1D partition, in a parallel SpMV operation. In a positive view, s2D thus can be seen as being close to 2D partitions in terms of flexibility, and being close 1D partitions in terms of computation/communication organization. We describe two methods that take partitions on the input and output vectors of SpMV and produce s2D partitions while reducing the total communication volume. The first method obtains optimal total communication volume, while the second one heuristically reduces this quantity and takes computational load balance into account. We demonstrate that the proposed partitioning method improves the performance of parallel SpMV operations both in theory and practice with respect to 1D and 2D partitionings

1.5D Parallel Sparse Matrix-Vector Multiply

International audienceThere are three common parallel sparse matrix-vector multiply algorithms: 1D 3 row-parallel, 1D column-parallel and 2D row-column-parallel. The 1D parallel algorithms offer the 4 advantage of having only one communication phase. On the other hand, the 2D parallel algorithm 5 is more scalable but it suffers from two communication phases. Here, we introduce a novel concept 6 of heterogeneous messages where a heterogeneous message may contain both input-vector entries 7 and partially computed output-vector entries. This concept not only leads to a decreased number of 8 messages, but also enables fusing the input-and output-communication phases into a single phase. 9 These findings are exploited to propose a 1.5D parallel sparse matrix-vector multiply algorithm 10 which is called local row-column-parallel. This proposed algorithm requires a constrained fine-grain 11 partitioning in which each fine-grain task is assigned to the processor that contains either its input-12 vector entry, or its output-vector entry, or both. We propose two methods to carry out the constrained 13 fine-grain partitioning. We conduct our experiments on a large set of test matrices to evaluate the 14 partitioning qualities and partitioning times of these proposed 1.5D methods. 15 Key words. sparse matrix partitioning, parallel sparse matrix-vector multiplication, directed 16 hypergraph model, bipartite vertex cover, combinatorial scientific computing 1