Showing papers by "University of Ljubljana, Faculty of Economics published in 1987"
01 Jan 1987
TL;DR: This paper describes an interesting generalization of the revised simplex method, which is to use hypermatrices, a set of sparse vectors represented as sets of pointers to the table of all different nonzero values of the matrix and corresponding row indices.
Abstract: Nearly all practical linear programming (LP) problems are sparse. Computer implementations of the revised simplex method for solution of LP problems depend heavily on the proper exploitation of sparsity. The most convenient way of doing this is to handle the matrix as a set of sparse vectors, one for each column. These sparse vectors can be represented as sets of pointers to the table of all different nonzero values of the matrix and corresponding row indices. In this paper we describe an interesting generalization of this approach, which is to use hypermatrices. In this method the matrix is divided into blocks which are stored in the way described above. Access to blocks is obtained through a full matrix of pointers, with null pointers where the blocks are without nonzero elements. This approach is based on the fact that the row indices within blocks can be stored using less storage than the row indices of the entire matrix. In this paper we also describe our design and experimental implementation of this hypermatrix approach within the LP package for the IBM PC XT, which we are currently developing.