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

TL;DR

This paper introduces a linear-time online algorithm for inferring edge-labeled graphs from walks, improving upon previous methods that required logarithmic factors, by leveraging palindrome detection techniques.

Contribution

It presents the first linear-time online algorithm for inferring path graphs from walks, utilizing Manacher's algorithm for maximal palindrome computation.

Findings

Algorithm runs in O(n) time for path graphs

Improves upon previous O(n log n) solutions

Uses palindrome detection for graph inference

Abstract

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.