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

@inproceedings{Narisada2018LinearTimeOA, title={Linear-Time Online Algorithm Inferring the Shortest Path from a Walk}, author={Shintaro Narisada and Diptarama Hendrian and Ryo Yoshinaka and Ayumi Shinohara}, booktitle={SPIRE}, year={2018} }

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 \(\mathrm {O}(n \log n)\) 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 \(\mathrm {O}(n)\) time, based on Manacher’s algorithm for computing all the maximal palindromes in a string.

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