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Fault Tolerant Depth First Search in Undirected Graphs: Simple Yet Efficient

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Abstract

Let G be an undirected graph. We address the problem of fault tolerant depth first search (DFS) tree defined as follows. Build a compact data structure that, given any set \({{\mathcal {F}}}\) of failed vertices or edges, can efficiently report a DFS tree of \(G{\backslash } {{\mathcal {F}}}\). We present an algorithm which is drastically simpler and yet more efficient than the current state-of-the-art algorithms for this problem. Additionally, for achieving efficiency, the current-state-of-the-algorithms have to crucially rely on sophisticated data structures. The simplicity of our algorithm also enables us to replace these sophisticated data structures with much simpler and lighter data structures that occupy optimal space and take optimal preprocessing time. Our algorithm for the fault tolerant DFS tree also leads to a better time complexity for maintaining a DFS tree in a fully dynamic environment.

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Notes

  1. One word stores \(\lceil \log m \rceil \) bits.

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Acknowledgements

Part of this research work was carried out while the first author was at Heinz Nixdorf Institute, on sabbatical leave from IIT Kanpur. His research work at the Heinz Nixdorf Institute was supported by a fellowship from Alexander von Humboldt Foundation. He is extremely grateful to Friedhelm Meyer auf der Heide who, as a host for this fellowship, provided him a highly supportive, encouraging, and free atmosphere conducive for this research work. The authors are thankful to one of the reviewers for providing very insightful comments.

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Authors and Affiliations

  1. Department of CSE, IIT Kanpur, Kanpur, 208016, India

    Surender Baswana, Shiv Gupta & Ayush Tulsyan

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  1. Surender Baswana
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  2. Shiv Gupta
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  3. Ayush Tulsyan
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Correspondence to Surender Baswana.

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A preliminary version of this article appeared in the Proceedings of 44th International Symposium on Mathematical Foundations of Computer Science (MFCS), August 26–30, 2019, Aachen, Germany [5].

This research work was partially supported by Alexander von Humboldt Foundation.

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Baswana, S., Gupta, S. & Tulsyan, A. Fault Tolerant Depth First Search in Undirected Graphs: Simple Yet Efficient. Algorithmica 84, 2028–2049 (2022). https://doi.org/10.1007/s00453-022-00947-7

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