@TechReport{Dartmouth:TR95-272, author = {Stavros G. Kolliopoulos and Clifford Stein}, title = {{Finding Real-Valued Single-Source Shortest Paths in o(n^3) Expected Time}}, institution = {Dartmouth College, Computer Science}, address = {Hanover, NH}, number = {PCS-TR95-272}, year = {1995}, month = {October}, URL = {http://www.cs.dartmouth.edu/reports/TR95-272.pdf}, abstract = { Given an $n$-vertex directed network $G$ with real costs on the edges and a designated source vertex $s$, we give a new algorithm to compute shortest paths from $s$. Our algorithm is a simple deterministic one with $O(n^2 \log n)$ expected running time over a large class of input distributions. The shortest path problem is an old and fundamental problem with a host of applications. Our algorithm is the first strongly-polynomial algorithm in over 35 years to improve upon some aspect of the running time of the celebrated Bellman-Ford algorithm for arbitrary networks, with any type of cost assignments. } }