@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 = jan,

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",

note = "17th Symposium on Mathematical Foundations of Computer Science, MFCS 1992 ; Conference date: 24-08-1992 Through 28-08-1992",

}