### 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 language | English |
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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 | |

Publication status | Published - Jan 1 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8889 |

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

*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