A Novel Heuristic Approach to Simplify Initial Graph of Maximum Flow Problem

Network maximum flow problem trying to find the maximum flow that can transmit from the source nodes to sink nodes. The purpose of this research is to improve and simplify the initial graph that given as a problem to solve by network maximum flow algorithm. Most of maximum flow algorithms solve the problem with finding route & transmitting based on basic feasible solution. In this paper، we attempt to present a new heuristic approach according to depth concept in graph to reduce the problem time complexity with removing arcs and nodes. This algorithm is compatible with multi-source multi-sink algorithms in the literature. Finally، to demonstrate applicability of the proposed approach، several test problems are first generated; then، the comparisons are carried out. The results show that the proposed heuristic can simplify the problem and consequently reduce the complexity of maximum flow problem