INFERRING A TREE FROM WALKS

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 col ors, 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 co nsider 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 pro blem turns to be NP-complete even if the number of colors is restricte d 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 fr om a single walk is known to be solvable in polynomial time.