The algebraic path problem revisited

Abstract

We derive an efficient linear simd architecture for the algebraic path problem (app). For a graph with n nodes, our array has n processors, each with 3n memory cells, and computes the result in 3n2 - 2n steps. Our array is ideally suited for vlsi, since the controls is simple and the memory can be implemented as fifos. i/o is straightforward, since the array is linear. It can be trivially adapted to run in multiple passes, and moreover, this version improves the work efficiency. For any constant α, the running time on n/α processors is no more than (α +2)n2. The work is no more than (1 + 2/α)n3 and can be made as close to n3 as desired by increasing α. © Springer-Verlag Berlin Heidelberg 1999.