An Efficient Algorithm for Row Minima Computations on Basic Reconfigurable Meshes

—A matrix A of size m œ n containing items from a totally ordered universe is termed monotone if, for every i, j, 1 ‹ i < j ‹ m, the minimum value in row j lies below or to the right of the minimum in row i. Monotone matrices, and variations thereof, are known to have many important applications. In particular, the problem of computing the row minima of a monotone matrix is of import in image processing, pattern recognition, text editing, facility location, optimization, and VLSI. Our first main contribution is to exhibit a number of nontrivial lower bounds for matrix search problems. These lower bound results hold for arbitrary, infinite, two-dimensional reconfigurable meshes as long as the input is pretiled onto a contiguous n œ n submesh thereof. Specifically, in this context, we show that every algorithm that solves the problem of computing the minimum of an n œ n matrix must take W(log log n) time. The same lower bound is shown to hold for the problem of computing the mi...

• Type: Journal
• Year: 1998
• Where: TPDS
• Authors: Koji Nakano, Stephan Olariu
• Keywords: Lower Bound, Matrix, Monotone Matrix, TPDS 1998