# Efficient Algorithms for Shortest Paths in Sparse Networks

@article{Johnson1977EfficientAF, title={Efficient Algorithms for Shortest Paths in Sparse Networks}, author={Donald B. Johnson}, journal={Journal of the ACM (JACM)}, year={1977}, volume={24}, pages={1 - 13} }

Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs. Known results which the results of this paper extend are surveyed briefly and analyzed. A new implementation for priority queues is employed, and a class of “arc set partition” algorithms is introduced. For the single source problem on networks with nonnegative arcs a running time of O(min(n1+1/k + e, n + e) log n)) is achieved, where there are n…

## 1,032 Citations

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## References

SHOWING 1-10 OF 50 REFERENCES

Finding the Lengths of All Shortest paths in N -Node Nonnegative-Distance Complete Networks Using 12N3 Additions and N3 Comparisons

- Computer ScienceJACM
- 1972

A (computer programming) algorithm is presented which is based on Dijkstra 's principle for finding the lengths of all shortest paths from either a fixed node or from all nodes in N-node…

A Shortest Path Algorithm for Edge-Sparse Graphs

- Computer ScienceJ. ACM
- 1976

An algorithm (FLOW) for finding the shortest distance from a given node S to each node X of a directed graph with nonnegative integer arc lengths less than or equal to WM is presented. FLOW is…

Shortcut in the decomposition algorithm for shortest paths in a network

- Computer Science
- 1969

A decomposition algorithm is proposed for use for use in finding the shortest path between the two nodes of every pair in a large n-node network, which requires less computer storage and fewer arithmetic operations than other known algorithms.

An algorithm for finding shortest routes from all source nodes to a given destination in general networks

- Computer Science
- 1970

This paper presents an algorithm for finding all shortest routes from all nodes to a given destination in iV-node general networks (in which the distances of arcs can be negative). If no negative…

On the Shortest Route Through a Network

- Computer Science
- 1960

This paper refines proposals to give what is believed to be the shortest procedure for finding the shortest route when it is little effort to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation.

On shortest paths and sorting

- Computer ScienceACM Annual Conference
- 1972

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.

ALL SHORTEST ROUTES FROM A FIXED ORIGIN IN A GRAPH

- Mathematics
- 1966

Abstract : A shortest route is sought between a fixed origin to other nodes in a graph when directed arc distances are given which may be positive, negative, or zero. This problem as stated includes…

A Note on Dijkstra's Shortest Path Algorithm

- PhysicsJACM
- 1973

An assertion that Dijkstra's algorithm for shortest paths (adapted to allow arcs of negative weight) runs in O(n)(supscrpt) steps is disproved by showing a set of networks which take O (O) 2 (n) 3 steps.

ALL SHORTEST ROUTES IN A GRAPH

- Mathematics
- 1966

Abstract : An inductive procedure on nodes is given that requires n(n-1)(n-2) comparison - addition operations to determine minimum routes between all nodes of a directed network. Arc distances may…

Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

- Computer ScienceCombinatorial Optimization
- 2001

Upper bounds on the number of steps in these algorithms are derived, and are shown to improve on the upper bounds of earlier algorithms.