Novel Effective Algorithm for Synchronization Problem in Directed Graph

Abstract

An effective algorithm for solving synchronization problem in directed graph is presented. The system is composed of vertices and edges. Entities are going through the system by given paths and can leave the vertex if all other entities which are going through this vertex have already arrived. The aim of this research is to create an algorithm for finding an optimal input vector of starting times of entities which gives minimal waiting time of entities in vertices and thus in a whole system. Asymptotic complexity of a given solution and using of brute-force method is discussed and compared. This algorithm is shown on an example from a field of train timetable problem.