Inferring a tree from walks
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.
KeywordsBinary Relation Small Tree Linear Chain Vertex Cover Finite Alphabet
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