The serial Jacobi algorithm (either one-sided or two-sided) for the computation of a singular value decomposition (SVD) of a general matrix has excellent numerical properties and parallelization potential, but it is considered to be the slowest method for computing the SVD. Even its parallelization with some parallel cyclic (static) ordering of subproblems does not lead to much improvement when...

Consider an p n pn processor mesh where, in addition to the local links, each row and column is enhanced by a COMMON CRCW bus. Assume that each processor stores an element of a commutative semigroup, and only k < n entries (in arbitrary positions) are nonzero. We wish to compute the sum of all entries. For this problem we easily obtain a lower time bound of (k) if k n. Our main result is an O(k...

One of the advantages of functional languages is the ability to use higher-order functions to guide the design of certain classes of algorithms. This paper is concerned with genetic algorithms (GAs) and their application to the solution of the single row routing (SRR) problem which is an important problem in the design of multilayer printed circuit boards (MPCBs). The paper presents a framework...

This paper studies a batch machine scheduling problem in which decisions on grouping jobs into batches and scheduling batches on parallel machines are jointly made. To address the problem, we model it as two-stage set-partitioning (TSSP) type formulation with exponential number of rows and columns. To find solutions, we propose a row-and-column generation method. The proposed method starts with...

In Placement Legalization, it is often assumed that (almost) all standard cells possess the same height and can therefore be aligned in cell rows , which then treated independently. However, this no longer true for recent technologies, where a substantial number of double- or even arbitrary multiple-row to expected. Due interdependencies between placements within several rows, legalization task...

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original row sparsity and row sparsity pattern. However, the confidence-constrained opt...

We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for “consistent” parallel processing of sparse outer products (column-row vector products) over several processors, in a communication-avoiding setting where each processor has a copy of the input. T...