# Shortest path algorithms

@article{Gallo1988ShortestPA,
title={Shortest path algorithms},
author={Giorgio Gallo and Stefano Pallottino},
journal={Annals of Operations Research},
year={1988},
volume={13},
pages={1-79}
}
• Published 1 December 1988
• Computer Science
• Annals of Operations Research
Theshortest path problem is considered from a computational point of view. Eight algorithms which solve theshortest path tree problem on directed graphs are presented, together with the results of wide-ranging experimentation designed to compare their relative performances on different graph topologies. The focus of this paper is on the implementation of the different data structures used in the algorithms. A "Pidgin Pascal" description of the algorithms is given, containing enough details to…
294 Citations
ITERATION ALGORITHM FOR SHORTEST PATH PROBLEMS ∗
An algorithm is proposed which is a deterministic version of Howard's policy iteration scheme, and it is shown that policy iteration is faster than the Bellman (or value iteration) algorithm.
Point-to-Point Shortest Path Algorithms with Preprocessing
A survey of some recent results on point-to-point shortest path algorithms and recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big.
Computation of the Reverse Shortest-Path Problem
• Mathematics, Computer Science
J. Glob. Optim.
• 2003
In this paper, for the general problem, the NP-completeness is shown, and for the cases of trees and the case of single source-terminal, polynomial-time algorithms are presented.
Shortest Path Algorithms between Theory and Practice
This thesis discusses a new single-source shortest-path algorithm that achieves the same $O(n \cdot m)$ time bound as the traditional Bellman-Ford-Moore algorithm but outperforms it and other state-of-the-art algorithms in practice in practice.
On the shortest path problem with negative cost cycles
• Computer Science
Comput. Optim. Appl.
• 2016
In this paper, the elementary single-source all-destinations shortest path problem is considered and two solution strategies are proposed to solve the problem under investigation and their theoretical properties are investigated.
Guided Search for the Shortest Path on Transportation Networks
• Computer Science
• 1996
A new approach is presented which guides the search of the shortest path algorithms under investigation and shows that the guided algorithm outperforms the original algorithms for transportation networks with Euclidean arc costs.
Choosing a Shortest Path AlgorithmTechnical Report CSE-95-004
• Computer Science
• 1995
This paper develops a theoretical indicator, H, that can be used to identify algorithms with poor performance and shows that using this theoretical guideline can result in reducing execution time signiicantly for various transportation networks.

## References

SHOWING 1-10 OF 40 REFERENCES
Implementation and efficiency of Moore-algorithms for the shortest route problem
• U. Pape
• Computer Science
Math. Program.
• 1974
The main objective of this paper is to show the strong relationship between an algorithm and its implementation and to show a variant of Moore's method seems to be most efficient for different types of graph structures.
A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees
• Computer Science
Networks
• 1979
The study shows that the procedures examined indeed exert a powerful influence on solution efficiency, with the identity of the best dependent upon the topology of the network and the range of the arc distance coefficients.
Shortest-path methods: Complexity, interrelations and new propositions
A computational method which consists of determining shortest paths on a finite sequence of partial graphs defined as the “growth of the original graph” is developed and allowed to interpret within the same framework several different well-known algorithms.
Efficient Algorithms for Shortest Paths in Sparse Networks
Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs, and a class of “arc set partition” algorithms is introduced.
SHORTEST PATH METHODS: A UNIFYING APPROACH
• Computer Science
• 1986
This analysis suggests a new classification of the shortest path algorithms, showing all the algorithms described to derive from one single prototype method, the difference between them depending only on the particular data structure used in their implementation.
A dual simplex algorithm for finding all shortest paths
• Computer Science
Networks
• 1981
The adaptation of the dual simplex algorithm to compute the shortest paths from node s results in an algorithm which has the flavor of a label-setting method, which generally does not require the examination of all the nodes of the network.
On shortest paths and sorting
It is shown how algorithms from sorting literature can be used to accomplish this part of the shortest path algorithm, and bounds on the largest possible amount of work are established.
Algorithm 562: Shortest Path Lengths [H]
This algorithm finding the shortest path lengths from a specific node to all other nodes in a network is a modification of Moore's algorithm, originally due to d'Esopo as reported by Pollack and Wiebenson and refined by Pape.