Quantum Algorithm for the Longest Trail Problem

TL;DR

This paper introduces a quantum algorithm designed to efficiently find the longest edge-simple path in a graph, significantly improving search times for complex graph traversal problems.

Contribution

The paper presents a novel quantum algorithm for the Longest Trail Problem with a specific exponential time complexity, advancing quantum approaches to graph algorithms.

Findings

Quantum algorithm runs in $O^*(1.728^m)$ time

Provides a new quantum approach to the Longest Trail Problem

Improves efficiency over classical algorithms for large graphs

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 $O^*(1.728^m)$.