ASSOCIATIVE SHORTEST AND LONGEST PATH PROBLEMS
Yukihiro Maruyama · Bulletin of informatics and cybernetics · 1999
In the paper we consider a wide class of shortest path problems where the length of a path is defined through various associative binary operations. Solving a system of two interrelated recursive equations, we simultaneously find both shortest and longest path lengths. We show the existence and uniqueness of the solution of the system. Further, we propose an algorithm which solves the class of shortest path problems.