Communication Dans Un Congrès Année : 2025

SAT-Based CEGAR Method for the Hamiltonian Cycle Problem Enhanced by Cut-Set Constraints

Ryoga Ohashi
Takehide Soh
Hidetomo Nabeshima
Mutsunori Banbara
Naoyuki Tamura

Résumé

In this paper, we propose an enhancement to the SAT-based counterexample-guided abstraction refinement (CEGAR) approach for solving the Hamiltonian Cycle Problem (HCP). Many SAT-based methods for HCP have been proposed, including a CEGAR-based method that repeatedly solves a relaxed version of HCP strengthened by counterexamples. However, when the counterexample space - represented by the full set of subcycle partitions - is large, it becomes difficult to find a solution. To address this, we introduce cut-set constraints in the refinement step, replacing traditional subcycle blocking constraints. Our evaluation shows that these cut-set constraints achieve equal or better reduction in the counterexample space, making it easier to find valid solutions. We further assessed performance using all 1001 instances from the FHCP challenge set and confirmed that the proposed method solved 937 instances within 1800 seconds, outperforming both the existing eager and CEGAR encodings (which solved at most 666 instances). This demonstrates the effectiveness of incorporating cut-set constraints into SAT-based CEGAR approaches.

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Dates et versions

hal-05219008 , version 1 (22-08-2025)

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Citer

Ryoga Ohashi, Takehide Soh, Daniel Le Berre, Hidetomo Nabeshima, Mutsunori Banbara, et al.. SAT-Based CEGAR Method for the Hamiltonian Cycle Problem Enhanced by Cut-Set Constraints. 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025), Aug 2025, Glasgow, United Kingdom. ⟨10.4230/LIPIcs.SAT.2025.24⟩. ⟨hal-05219008⟩
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