Depth-First Search Performance in a Random Digraph with Geometric Degree Distribution

Authors Philippe Jacquet , Svante Janson

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Author Details

Philippe Jacquet
  • Inria Saclay Ile de France, France
Svante Janson
  • Department of Mathematics, Uppsala University, Uppsala, Sweden


We thank Donald Knuth for posing us questions and conjectures that led to the present paper.

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Philippe Jacquet and Svante Janson. Depth-First Search Performance in a Random Digraph with Geometric Degree Distribution. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We present an analysis of the depth-first search algorithm in a random digraph model with geometric outdegree distribution. We give also some extensions to general outdegree distributions. This problem posed by Donald Knuth in his next to appear volume of The Art of Computer Programming gives interesting insight in one of the most elegant and efficient algorithm for graph analysis due to Tarjan.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Combinatorics
  • Depth-First Search
  • Random Digraphs


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