A latin square is an n x n square matrix each of which cells contains a symbol chosen from the set 11,2, ... ,n]; each symbol occurs exactly oncl~ in each row or column of the matrix. A partial latin square is a latin square in which some cells are unoccupied. We consider the problem of obtaining necessary and sufficient conditions for a partial latin square to be completed to a latin square. F...

This report considers the problem of writing data distribution independent (DDI) programs in order to eliminate or reduce initial data redistribution overheads for distributed memory parallel computers. The functionality and execution time of DDI programs are independent of initial data distributions. First, modular mappings, which can be used to derive many equally optimal ant1 functionally eq...

We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property. Our primary goal in this paper is to address the structure prediction problem for matrices satisfying a weaker assumption...

One of the graph theoretic approaches of channel assignment for cellular networks is routing a pair of nodes arranged in a single-row axis called single-row routing problem. The network with nodes representing caller and receiver is to be transformed into a single-row network efficiently is proposed. The connected graph derived from the base network is presented using incidence matrix. The rows...

This paper presents a fast incremental algorithm for low rank approximations or dimensionality reduction of matrices. Assuming that matrices have double-sided type of decomposition, we can set up an incremental solution that constitutes two coupled eigenmodels and thus a two-step updating procedure. At each step, we first represent row-row or column-column covariance matrix as the form of eigen...

Sparse matrices are a core component in many numerical simulations, and their efficiency is essential to achieving high performance. Dynamic sparse-matrix allocation (insertion) can benefit a number of problems such as sparse-matrix factorization, sparse-matrix-matrix addition, static analysis (e.g., points-to analysis), computing transitive closure, and other graph algorithms. Existing sparse-...

We investigate the balancing of distributed compressed storage of large sparse matrices on a massively parallel computer. For fast computation of matrix{vector and matrix{matrix products on a rectangular processor array with e cient communications along its rows and columns we require that the nonzero elements of each matrix row or column be distributed among the processors located within the s...

In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one may generalize that concept as a block partition of a complex square matrix s.t. each block has constant row sum. It is well known that replacing each block ...

We present an algorithm for general sparse matrix-matrix multiplication (SpGEMM) on many-core architectures, such as GPUs. SpGEMM is implemented by iterative row merging, similar to merge sort, except that elements with duplicate column indices are aggregated on the fly. The main kernel merges small numbers of sparse rows at once using sub-warps of threads to realize an early compression effect...

This is an attempt to devise a memory efficient WDR (Wavelet Difference Reduction) algorithm by decomposing a matrix using customized Echelon algorithm and applying WDR on it in parts. The standard process of WDR algorithm requires the entire matrix to be available in RAM (random access memory) which might not be feasible always or for a longer duration till the entire matrix is encoded. This i...