  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 $O(n \log n)$ 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.
