Inferring a Tree from Walks
Osamu Maruyama, Satoru Miyano, Satoru Miyano, 宮野, 悟 · QIR (Kyushu University Institutional Repository) (Kyushu University) · 1991
A walk in 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 in 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. 1.