Pre-treatment of path problems with required lengths

Abstract

Path problem is a core problem of graph theory, and its representative one is the shortest path problem. But in many cases the most reasonable solution of path problem is some paths with a required length rather than the shortest one. For the path problem with required length, we propose a pretreatment technology – simplification. We found the shortest path model, and reveal and summary properties of the model as a theorem which reflects relationships between parameters of the model and path lengths. Base on the path model, we design a simple algorithm to simplify the graph for reducing difficulty of the path problem.