QUBO formulation for the Snake-in-the-box and Coil-in-the-box problems

TL;DR

This paper introduces the first QUBO formulations for the NP-Hard Snake-in-the-box and Coil-in-the-box problems, enabling their solution via classical and quantum methods, and also proposes a new formulation for the Maximum Common Induced Sub-graph problem.

Contribution

The paper presents novel QUBO formulations for SITB, CITB, and Maximum Common Induced Sub-graph problems, with proven correctness and successful testing on classical and quantum solvers.

Findings

Successfully formulated SITB and CITB as QUBO problems.

Achieved best solutions for problems up to 5 dimensions.

Validated formulations through proofs and solver experiments.

Abstract

This paper present the first QUBO formulations for the Snake-in-the-box (SITB) and Coil-in-the-box (CITB) problems. Both formulations are also capable of solving the NP-Hard problems of Maximum induced path and Maximum induced cylce respectively. In the process we also found a new QUBO formulation for the Maximum Common Induced Sub-graph problem. We proved the correctness of our formulations for the SITB, CITB and Maximum Common Sub-graph problem, and tested the formulations of the SITB and CITB in both classical and quantum solvers, being able to get the best solution for up to 5 dimensions.