## Single-Source Shortest-Paths on Arbitrary Directed Graphs in Linear Average-Case Time (2001)

Venue: | In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms |

Citations: | 28 - 5 self |

### BibTeX

@INPROCEEDINGS{Meyer01single-sourceshortest-paths,

author = {Ulrich Meyer},

title = {Single-Source Shortest-Paths on Arbitrary Directed Graphs in Linear Average-Case Time},

booktitle = {In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms},

year = {2001},

pages = {797--806},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

The quest for a linear-time single-source shortest-path (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an O(n + m) time RAM algorithm for undirected graphs with n nodes, m edges and integer edge weights in f0; : : : ; 2 w 1g where w denotes the word length, the currently best time bound for directed sparse graphs on a RAM is O(n + m log log n). In the present paper we study the average-case complexity of SSSP. We give a simple algorithm for arbitrary directed graphs with random edge weights uniformly distributed in [0; 1] and show that it needs linear time O(n + m) with high probability. 1 Introduction The single-source shortest-path problem (SSSP) is a fundamental and well-studied combinatorial optimization problem with many practical and theoretical applications [1]. Let G = (V; E) be a directed graph, jV j = n, jEj = m, let s be a distinguished vertex of the graph, and c be a function assigning a n...