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Depth-First Search Performance in Random Digraphs

Authors Philippe Jacquet , Svante Janson

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Author Details

Philippe Jacquet
  • Inria Saclay Ile de France, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
Svante Janson
  • Department of Mathematics, Uppsala University, Sweden

Funding

  • Janson, Svante: Supported by the Knut and Alice Wallenberg Foundation and the Swedish Research Council (VR).

Cite AsGet BibTex

Philippe Jacquet and Svante Janson. Depth-First Search Performance in Random Digraphs. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.30

Abstract

We present an analysis of the depth-first search algorithm in a random digraph model with independent outdegrees having an arbitrary distribution with finite variance. The results include asymptotics for the distribution of the stack index and depths of the search. The search yields a series of trees of finite size before and after the exploration of a giant tree. Our analysis mainly concerns the giant tree. Most results are first order. This analysis proposed 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
  • Mathematics of computing → Trees
Keywords
  • Depth First Search
  • random digraph
  • Analysis of Algorithms

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