Improved processor bounds for algebraic and combinatorial problems in RNC

Abstract

of Results Our two main results improve the processor bounds of two important problems: Problem 1: Computing the exact inverse and the determinant of an n x n matrix whose entries are L-bit integers, L =nO(l). The improved solutions maintain the best running time (O(log2 n), O(log3 n), resp.) for the two problems. A solution to Problem 1 is used in a number of parallel algorithms for algebraic problems as··well as for solving Problem 2. A solution for Problem 2 is used in parallel algorithms for severai combinatorial problems. Consequently, the new algorithms lead to improved solutions to several algebraic and combinatorial problems. We state the bounds in the arithmetic circuit model (0A (f(n))) in which each arithmetic operation is performed in one unit of time and in the (more realistic) Boolean circuit model (OB (g(n))) in which each Boolean operation takes one unit of time: New Algorithms Previous best bound Problem 1 OA(n 2 .