Elsevier

Journal of Algorithms

Volume 34, Issue 1, January 2000, Pages 148-176
Journal of Algorithms

Regular Article
Average Costs of a Graph Exploration: Upper and Lower Bounds

https://doi.org/10.1006/jagm.1999.1053Get rights and content

Abstract

We consider the exploration of random digraphs. We give upper and lower bounds for the expected number of edges traversed during an exploration. This result implies a lower bound for the expected running time of a wide class of algorithms, e.g., breadth-first-search, depth-first-search, and algorithms to determine a minimum spanning tree or to solve the single source shortest paths problem in a weighted digraph. Furthermore, we investigate the connectedness of nonhomogeneous random digraphs and we point out the relationship with the exploration algorithms.

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This work was in part supported by the Schweizerischer Nationalfond, Project 2100-043537.95.

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