# Linear-Time Online Algorithm Inferring the Shortest Path from a Walk

We consider the problem of inferring an edge-labeled graph from the sequence of edge labels seen in a walk of that graph. It has been known that this problem is solvable in O(n n) time when the targets are path or cycle graphs. This paper presents an online algorithm for the problem of this restricted case that runs in O(n) time, based on Manacher's algorithm for computing all the maximal palindromes in a string.

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