Inferring a tree from walks

Osamu Maruyama, Satoru Miyano

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)289-300
Number of pages12
JournalTheoretical Computer Science
Volume161
Issue number1-2
DOIs
Publication statusPublished - Jul 15 1996

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Walk
Color
Partial
Polynomials
NP-complete problem
Strings
Edge-colored Graph
Path
Undirected Graph
Polynomial time

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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

In: Theoretical Computer Science, Vol. 161, No. 1-2, 15.07.1996, p. 289-300.

Research output: Contribution to journalArticle

Maruyama, Osamu ; Miyano, Satoru. / Inferring a tree from walks. In: Theoretical Computer Science. 1996 ; Vol. 161, No. 1-2. pp. 289-300.
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