Parallel Iterative Algorithms for Solving Path Problems

Abstract

Path problems are a family of optimization and enumeration problems involving the determination of paths in directed graphs. In this paper few parallel iterative algorithms for solving path problems are developed. More precisely, the considered algorithms are parallelized counterparts of the classical iterative methods, such as Jacobi or Gauss-Seidel. The underlying model of computation is a tightly coupled multiprocessor. It is shown that the algorithms obtain the required solution after a finite number of iterations. For each algorithm, the computational complexity of a single iteration is estimated, and an upper bound for the number of iterations is established. On the basis of these results the algorithms are compared.