## A shortest path algorithm for real-weighted undirected graphs (1985)

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Venue: | in 13th ACMSIAM Symp. on Discrete Algs |

Citations: | 12 - 3 self |

### BibTeX

@ARTICLE{Pettie85ashortest,

author = {Seth Pettie and Vijaya Ramachandran},

title = {A shortest path algorithm for real-weighted undirected graphs},

journal = {in 13th ACMSIAM Symp. on Discrete Algs},

year = {1985},

volume = {34},

pages = {267--276}

}

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### Abstract

Abstract. We present a new scheme for computing shortest paths on real-weighted undirected graphs in the fundamental comparison-addition model. In an efficient preprocessing phase our algorithm creates a linear-size structure that facilitates single-source shortest path computations in O(m log α) time, where α = α(m, n) is the very slowly growing inverse-Ackermann function, m the number of edges, and n the number of vertices. As special cases our algorithm implies new bounds on both the all-pairs and single-source shortest paths problems. We solve the all-pairs problem in O(mnlog α(m, n)) time and, if the ratio between the maximum and minimum edge lengths is bounded by n (log n)O(1) , we can solve the single-source problem in O(m + nlog log n) time. Both these results are theoretical improvements over Dijkstra’s algorithm, which was the previous best for real weighted undirected graphs. Our algorithm takes the hierarchy-based approach invented by Thorup. Key words. single-source shortest paths, all-pairs shortest paths, undirected graphs, Dijkstra’s