### Abstract

A walk on an undirected edge-colored graph G is a path containing all edges of G. The tree inference from a walk is, given a string x of colors, finding the smallest tree that realizes a walk whose sequence of edge-colors coincides with x. We prove that the problem is solvable in O(n) time, where n is the length of a given string. We furthermore consider the problem of inferring a tree from a finite number of partial walks, where a partial walk on G is a path in G. We show that the problem turns to be NP-complete even if the number of colors is restricted to 3. It is also shown that the problem of inferring a linear chain from partial walks is NP-complete, while the linear chain inference from a single walk is known to be solvable in polynomial time.

Original language | English |
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Pages (from-to) | 289-300 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 161 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jul 15 1996 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*161*(1-2), 289-300. https://doi.org/10.1016/0304-3975(95)00156-5

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 161, no. 1-2, pp. 289-300. https://doi.org/10.1016/0304-3975(95)00156-5

}

TY - JOUR

T1 - Inferring a tree from walks

AU - Maruyama, Osamu

AU - Miyano, Satoru

PY - 1996/7/15

Y1 - 1996/7/15

N2 - A walk on an undirected edge-colored graph G is a path containing all edges of G. The tree inference from a walk is, given a string x of colors, finding the smallest tree that realizes a walk whose sequence of edge-colors coincides with x. We prove that the problem is solvable in O(n) time, where n is the length of a given string. We furthermore consider the problem of inferring a tree from a finite number of partial walks, where a partial walk on G is a path in G. We show that the problem turns to be NP-complete even if the number of colors is restricted to 3. It is also shown that the problem of inferring a linear chain from partial walks is NP-complete, while the linear chain inference from a single walk is known to be solvable in polynomial time.

AB - A walk on an undirected edge-colored graph G is a path containing all edges of G. The tree inference from a walk is, given a string x of colors, finding the smallest tree that realizes a walk whose sequence of edge-colors coincides with x. We prove that the problem is solvable in O(n) time, where n is the length of a given string. We furthermore consider the problem of inferring a tree from a finite number of partial walks, where a partial walk on G is a path in G. We show that the problem turns to be NP-complete even if the number of colors is restricted to 3. It is also shown that the problem of inferring a linear chain from partial walks is NP-complete, while the linear chain inference from a single walk is known to be solvable in polynomial time.

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UR - http://www.scopus.com/inward/citedby.url?scp=0030182823&partnerID=8YFLogxK

U2 - 10.1016/0304-3975(95)00156-5

DO - 10.1016/0304-3975(95)00156-5

M3 - Article

AN - SCOPUS:0030182823

VL - 161

SP - 289

EP - 300

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -