Gaussian block algorithms for solving path problems

Path problems are a family of optimization and enumeration problems that reduce to determination or evaluation of paths in a directed graph. In this paper we give a convenient algebraic description of block algorithms for solving path problems. We also develop block versions of two Gaussian algorithms, which are counterparts of the conventional Jordan and escalator method respectively. The correctness of the two considered block algorithms is discussed, and their complexity is analyzed. A parallel implementation of the block Jordan algorithm on a transputer network is presented, and the obtained experimental results are listed.