Quantum Algorithm for the Longest Trail Problem

Abstract

We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can occur several times. The running time of our algorithm is $O^{\ast }(1.728^m)$.

RuFiDim 2021. arXiv admin note: substantial text overlap with arXiv:2112.13319