Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-shortest Induced Paths

09/30/2021

∙

by   Yung-Chung Chiu, et al.

∙

0

∙

share

For vertices u and v of an n-vertex graph G, a uv-trail of G is an induced uv-path of G that is not a shortest uv-path of G. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in O(n^18) time, to either output a uv-trail of G or ensure that G admits no uv-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of n^2× n^2 Boolean matrices, leading to a largely improved O(n^4.75)-time algorithm.