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Encyclopedia of Algorithms pp 1996–1999Cite as

Single-Source Shortest Paths

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Years and Authors of Summarized Original Work

  • 1999; Thorup

Problem Definition

The single-source shortest path problem (SSSP) is, given a graph G = (V, E, l) and a source vertex s ∈ V, to find the shortest path from s to every v ∈ V . The difficulty of the problem depends on whether the graph is directed or undirected and the assumptions placed on the length function ℓ. In the most general situation, \(l : E \rightarrow \mathbb{R}\) assigns arbitrary (positive and negative) real lengths. The algorithms of Bellman-Ford and Edmonds [1, 4] may be applied in this situation and have running times of roughly O(mn), (Edmonds’s algorithm works for undirected graphs and presumes that there are no negative length simple cycles.) where m =  | E | and n =  | V | are the number of edges and vertices. If ℓ assigns only nonnegative real edge lengths, then the algorithms of Dijkstra and Pettie-Ramachandran [4, 13] may be applied on directed and undirected graphs, respectively. These algorithms include...

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Authors and Affiliations

  1. Electrical Engineering and Computer Science (EECS) Department, University of Michigan, Ann Arbor, MI, USA

    Seth Pettie

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  1. Seth Pettie
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Correspondence to Seth Pettie .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Pettie, S. (2016). Single-Source Shortest Paths. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_377

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