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

Research output: Chapter in Book/Report/Conference proceedingChapter

8 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 n/2Ω(√ log n) 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 languageEnglish
Title of host publicationAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
EditorsHee-Kap Ahn, Chan-Su Shin
PublisherSpringer Verlag
Pages553-564
Number of pages12
ISBN (Electronic)9783319130743
DOIs
Publication statusPublished - Jan 1 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8889
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Asano, T., Izumi, T., Kiyomi, M., Konagaya, M., Ono, H., Otachi, Y., ... 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/10.1007/978-3-319-13075-044