Depth-first search using O(n) bits

Tetsuo Asano; Taisuke Izumi; Masashi Kiyomi; Matsuo Konagaya; Hirotaka Ono; Yota Otachi; Pascal Schweitzer; Jun Tarui; Ryuhei Uehara

doi:10.1007/978-3-319-13075-0_44

Depth-first search using O(n) bits

Tetsuo Asano, Taisuke Izumi, Masashi Kiyomi, Matsuo Konagaya, Hirotaka Ono, Yota Otachi, Pascal Schweitzer, Jun Tarui, Ryuhei Uehara

mathematics and information

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

16 Citations (Scopus)

Abstract

We provide algorithms performing Depth-First Search (DFS) on a directed or undirected graph with n vertices and m edges using only O(n) bits. One algorithm uses O(n) bits and runs in O(mlog n) time. Another algorithm uses n+o(n) bits and runs in polynomial time. Furthermore, we show that DFS on a directed acyclic graph can be done in space [Formula presented], and in polynomial time, and we also give a simple linear-time O(log n)-space algorithm for the depth-first traversal of an undirected tree. Finally, we also show that for a graph having an O(1)-size feedback set, DFS can be done in O(log n) space. Our algorithms are based on the analysis of properties of DFS and applications of the s-t connectivity algorithms due to Reingold and Barnes et al., both of which run in sublinear space.

Original language	English
Title of host publication	Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
Editors	Hee-Kap Ahn, Chan-Su Shin
Publisher	Springer Verlag
Pages	553-564
Number of pages	12
ISBN (Electronic)	9783319130743
DOIs	https://doi.org/10.1007/978-3-319-13075-0_44
Publication status	Published - 2014
Event	25th International Symposium on Algorithms and Computation, ISAAC 2014 - Jeonju, Korea, Republic of Duration: Dec 15 2014 → Dec 17 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8889
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	25th International Symposium on Algorithms and Computation, ISAAC 2014
Country/Territory	Korea, Republic of
City	Jeonju
Period	12/15/14 → 12/17/14

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-13075-0_44

Cite this

Asano, T., Izumi, T., Kiyomi, M., Konagaya, M., Ono, H., Otachi, Y., Schweitzer, P., Tarui, J., & Uehara, R. (2014). Depth-first search using O(n) bits. In H-K. Ahn, & C-S. Shin (Eds.), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings (pp. 553-564). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_44

Depth-first search using O(n) bits. / Asano, Tetsuo; Izumi, Taisuke; Kiyomi, Masashi; Konagaya, Matsuo; Ono, Hirotaka; Otachi, Yota; Schweitzer, Pascal; Tarui, Jun; Uehara, Ryuhei.

Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. ed. / Hee-Kap Ahn; Chan-Su Shin. Springer Verlag, 2014. p. 553-564 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Asano, T, Izumi, T, Kiyomi, M, Konagaya, M, Ono, H, Otachi, Y, Schweitzer, P, Tarui, J & Uehara, R 2014, Depth-first search using O(n) bits. in H-K Ahn & C-S Shin (eds), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8889, Springer Verlag, pp. 553-564, 25th International Symposium on Algorithms and Computation, ISAAC 2014, Jeonju, Korea, Republic of, 12/15/14. https://doi.org/10.1007/978-3-319-13075-0_44

Asano T, Izumi T, Kiyomi M, Konagaya M, Ono H, Otachi Y et al. Depth-first search using O(n) bits. In Ahn H-K, Shin C-S, editors, Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. Springer Verlag. 2014. p. 553-564. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-13075-0_44

Asano, Tetsuo ; Izumi, Taisuke ; Kiyomi, Masashi ; Konagaya, Matsuo ; Ono, Hirotaka ; Otachi, Yota ; Schweitzer, Pascal ; Tarui, Jun ; Uehara, Ryuhei. / Depth-first search using O(n) bits. Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. editor / Hee-Kap Ahn ; Chan-Su Shin. Springer Verlag, 2014. pp. 553-564 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AU - Schweitzer, Pascal

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AB - We provide algorithms performing Depth-First Search (DFS) on a directed or undirected graph with n vertices and m edges using only O(n) bits. One algorithm uses O(n) bits and runs in O(mlog n) time. Another algorithm uses n+o(n) bits and runs in polynomial time. Furthermore, we show that DFS on a directed acyclic graph can be done in space [Formula presented], and in polynomial time, and we also give a simple linear-time O(log n)-space algorithm for the depth-first traversal of an undirected tree. Finally, we also show that for a graph having an O(1)-size feedback set, DFS can be done in O(log n) space. Our algorithms are based on the analysis of properties of DFS and applications of the s-t connectivity algorithms due to Reingold and Barnes et al., both of which run in sublinear space.

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Depth-first search using O(n) bits

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