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 |
|---|---|
| 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) |
|---|---|
| Volume | 629 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992 |
|---|---|
| Country | Czech Republic |
| City | Prague |
| Period | 8/24/92 → 8/28/92 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
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 proceeding › Conference contribution
}
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.
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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 -