Inferring a tree from walks

Osamu Maruyama, Satoru Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationMathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings
EditorsIvan M. Havel, Vaclav Koubek
PublisherSpringer Verlag
Pages383-391
Number of pages9
ISBN (Print)9783540558088
Publication statusPublished - Jan 1 1992
Event17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992 - Prague, Czech Republic
Duration: Aug 24 1992Aug 28 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume629 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992
CountryCzech Republic
CityPrague
Period8/24/928/28/92

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Maruyama, O., & Miyano, S. (1992). Inferring a tree from walks. In I. M. Havel, & V. Koubek (Eds.), 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.

Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings. ed. / Ivan M. Havel; Vaclav Koubek. Springer Verlag, 1992. p. 383-391 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 629 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Maruyama, O & Miyano, S 1992, Inferring a tree from walks. in IM Havel & V Koubek (eds), 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.
Maruyama O, Miyano S. Inferring a tree from walks. In Havel IM, Koubek V, editors, Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings. Springer Verlag. 1992. p. 383-391. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Maruyama, Osamu ; Miyano, Satoru. / Inferring a tree from walks. Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings. editor / Ivan M. Havel ; Vaclav Koubek. Springer Verlag, 1992. pp. 383-391 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{049423299a634734b586192e6a2cd12f,
title = "Inferring a tree from walks",
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.",
author = "Osamu Maruyama and Satoru Miyano",
year = "1992",
month = "1",
day = "1",
language = "English",
isbn = "9783540558088",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "383--391",
editor = "Havel, {Ivan M.} and Vaclav Koubek",
booktitle = "Mathematical Foundations of Computer Science 1992 - 17 International Symposium, Proceedings",
address = "Germany",

}

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 -