### Abstract

A walk of an edge-colored undirected graph G is a path which contains all edges in G. We show an O(n log n) time algorithm for finding the smallest tree from a walk which allows the walk. If the alphabet of colors is fixed, the algorithm runs in O(n) time. Further, we consider the problem of finding the smallest tree from partial walks, where a partial walk of G is a path in G. We prove that the problem turns to be NP-complete. We also show that inferring the smallest linear chain from partial walks is NP-complete, while the problem of inferring the smallest linear chain from a single walk is known to be solvable in polynomial time.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings |

Editors | Ivan M. Havel, Vaclav Koubek |

Publisher | Springer Verlag |

Pages | 383-391 |

Number of pages | 9 |

ISBN (Print) | 9783540558088 |

Publication status | Published - Jan 1 1992 |

Event | 17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992 - Prague, Czech Republic Duration: Aug 24 1992 → Aug 28 1992 |

### 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 | 629 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992 |
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Country | Czech Republic |

City | Prague |

Period | 8/24/92 → 8/28/92 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings*(pp. 383-391). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 629 LNCS). Springer Verlag.

**Inferring a tree from walks.** / Maruyama, Osamu; Miyano, Satoru.

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

*Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 629 LNCS, Springer Verlag, pp. 383-391, 17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992, Prague, Czech Republic, 8/24/92.

}

TY - GEN

T1 - Inferring a tree from walks

AU - Maruyama, Osamu

AU - Miyano, Satoru

PY - 1992/1/1

Y1 - 1992/1/1

N2 - A walk of an edge-colored undirected graph G is a path which contains all edges in G. We show an O(n log n) time algorithm for finding the smallest tree from a walk which allows the walk. If the alphabet of colors is fixed, the algorithm runs in O(n) time. Further, we consider the problem of finding the smallest tree from partial walks, where a partial walk of G is a path in G. We prove that the problem turns to be NP-complete. We also show that inferring the smallest linear chain from partial walks is NP-complete, while the problem of inferring the smallest linear chain from a single walk is known to be solvable in polynomial time.

AB - A walk of an edge-colored undirected graph G is a path which contains all edges in G. We show an O(n log n) time algorithm for finding the smallest tree from a walk which allows the walk. If the alphabet of colors is fixed, the algorithm runs in O(n) time. Further, we consider the problem of finding the smallest tree from partial walks, where a partial walk of G is a path in G. We prove that the problem turns to be NP-complete. We also show that inferring the smallest linear chain from partial walks is NP-complete, while the problem of inferring the smallest linear chain from a single walk is known to be solvable in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=84947938265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947938265&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84947938265

SN - 9783540558088

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 383

EP - 391

BT - Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings

A2 - Havel, Ivan M.

A2 - Koubek, Vaclav

PB - Springer Verlag

ER -