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European Symposium on Algorithms

ESA 1994: Algorithms — ESA '94 pp 343–353Cite as

On the structure of DFS-forests on directed graphs and the dynamic maintenance of DFS on DAG's

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

Abstract

In this paper we provide a characterization of a DFS-forest on directed graphs in terms of a relaxed planar embedding of its structure.

We propose an incremental algorithm, based on that characterization, to maintain a DFS-forest in a directed acyclic graph with n nodes and m edges, achieving O(nm) total time in the worst case for any sequence of arc insertions, that is O(n) amortized time per arc insertion in a sequence of Θ(m) such operations. This favorably compares with the time required to recompute DFS from scratch by using Tarjan's Θ(n+m) algorithm [19].

The graph is represented by means of adjacency lists and the dfs tree is maintained by using for each node a pointer to its parent, and a rank according to a suitable ordering: the whole data structure requires O(n+ m) space.

This is the first algorithm for dynamic DFS for nontrivial classes of graphs.

Partially supported by the ESPRIT Basic Research Action no.7141 (Alcom II) and by MURST national project “Algoritmi e Strutture di Calcolo”.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, via Salaria 113, I-00198, Roma, Italy

    Paolo G. Franciosa

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, I-00133, Roma, Italy

    Giorgio Gambosi

  3. Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, via Vetoio, I-67010, Coppito (AQ), Italy

    Umberto Nanni

Authors
  1. Paolo G. Franciosa
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  2. Giorgio Gambosi
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  3. Umberto Nanni
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Franciosa, P.G., Gambosi, G., Nanni, U. (1994). On the structure of DFS-forests on directed graphs and the dynamic maintenance of DFS on DAG's. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049421

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  • DOI: https://doi.org/10.1007/BFb0049421

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

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