LIPIcs.AofA.2024.30.pdf
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Depth-First Search Performance in Random Digraphs
Authors
Philippe Jacquet 
,
Svante Janson
-
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Volume:
35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-07-18
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- Inria Saclay Ile de France, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
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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
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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References
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Jürgen Bennies and Götz Kersting. A random walk approach to galton-watson trees. J. Theoret. Probab., 3:777-803, 2000.
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Sahar Diskin and Michael Krivelevich. On the performance of the depth first search algorithm in supercritical random graphs. Electron. J. Combin., 3, 2022.
-
Nathanaël Enriquez, Gabriel Faraud, and Laurent Ménard. Limiting shape of the depth first search tree in an erdős-rényi graph. Random Structures Algorithms, 2:501-516, 2020.
-
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard, and Nathan Noiry. Depth first exploration of a configuration model. Electron. J. Probab., 53, 2022.
-
Jean-François Le Gall and Yves Le Jan. Branching processes in lévy processes: the exploration process. Ann. Probab., 1:213-252, 1998.
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Philippe Jacquet and Svante Janson. Depth-first search performance in a random digraph with geometric outdegree distribution. La Matematica, 2024.
- Donald E. Knuth. The Art of Computer Programming. Preliminary draft, https://cs.stanford.edu/~knuth/fasc12a.ps.gz, 2022.
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Michael Krivelevich and Benny Sudakov. The phase transition in random graphs: a simple proof. Random Structures Algorithms, 2:131-138, 2013.
-
Jayant Madhavan, David Ko, Łucja Kot, Vignesh Ganapathy, Alex Rasmussen, and Alon Halevy. Google’s deep web crawl. Proceedings of the VLDB Endowment, 2:1241-1252, 2208.