Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem

• URL: http://arxiv.org/abs/2311.10941v1
• Date: Sat, 18 Nov 2023 02:36:10 GMT
• Title: Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem
• Authors: Giuseppe Corrente, Carlo Vincenzo Stanzione and Vittoria Stanzione
• Abstract summary: Hamiltonian cycle problem (HCP) consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve aHCP, using different models of computations and especially the probabilistic and quantum ones.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a Hamiltonian cycle problem, using different models of computations and especially the probabilistic and quantum ones. Starting from the classical probabilistic approach of random walks, we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine (QTM), which can be a useful conceptual project tool for quantum algorithms. Introducing several constraints to the graphs, our analysis leads to not-exponential speedup improvements to the best-known algorithms. In particular, the results are based on bounded degree graphs (graphs with nodes having a maximum number of edges) and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms.

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