# Inferring a tree from walks

Conference paper

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## 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.

## Keywords

Binary Relation Small Tree Linear Chain Vertex Cover Finite Alphabet
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1992