Proper arrangement of facility layout is a key issue in management that influences efficiency and the profitability of the manufacturing systems. Parallel Row Ordering Problem (PROP) is a special case of facility layout problem and consists of looking for the best location of n facilities while similar facilities (facilities which has some characteristics in common) should be arranged in a row ...

In this paper, we consider the problem of nding llpreserving ordering of a sparse symmetric and positive de nite matrix such that the reordered matrix is suitable for parallel factorization. We extended the unitcost ll-preserving ordering into a generalized class that can adopt various aspects in parallel factorization, such as computation, communication and algorithmic diversity. Based on the ...

The matrix chain ordering problem is to find the cheapest way to multiply a chain of n matrices, where the matrices are pairwise compatible but of varying dimensions. Here we give several new parallel algorithms including O(lg3 n)-time and n/lgn-processor algorithms for solving the matrix chain ordering problem and for solving an optimal triangulation problem of convex polygons on the common CR...

We suggest a new variant of a row layout problem: Find an ordering of n departments with given lengths such that the total weighted sum of their distances to a given checkpoint is minimized. The Checkpoint Ordering Problem (COP) is both of theoretical and practical interest. It has several applications and is conceptually related to some well-studied combinatorial optimization problems, namely ...

The row-by-row frontal method may be used to solve general large sparse linear systems of equations. By partitioning the matrix into (nearly) independent blocks and applying the frontal method to each block, a coarse-grained parallel frontal algorithm is obtained. The success of this approach depends on preordering the matrix. This can be done in two stages, (1) order the matrix to bordered blo...

We study a type of linear placement problem arising in detailed placement optimization of a given cell row in the presence of white-space (extra sites). In this single-row placement problem, the cell order is fixed within the row; all cells in other rows are also fixed. We give the first solutions to the single-row problem: (i) a dynamic programming technique with time complexity O(m2) where m ...

We study the largest values of the rth row of Stern’s diatomic array. In particular, we prove some conjectures of Lansing. Our main tool is the connection between the Stern sequence, alternating binary expansions, and continuants. This allows us to reduce the problem of ordering the elements of the Stern sequence to the problem of ordering continuants. We describe an operation that increases th...

We consider a certain class of parallel program segments in which the order of messages sent affects the completion time. We give characterization of these parallel program segments and propose a solution to minimize the completion time. With a sample parallel program, we experimentally evaluate the effect of the solution on a PC cluster.