그래프 감소를 위한 auction 알고리즘에 관한 연구

A study on auctio algorithms for reduced graph

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/all destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithm with O(n min{m, nlogn}) and O(n$^{2}$) running time.