Academic Journal
Interactive Exploration of the Hamiltonian Problem with Z3 and the Keçeci Layout
| Τίτλος: | Interactive Exploration of the Hamiltonian Problem with Z3 and the Keçeci Layout |
|---|---|
| Συγγραφείς: | Mehmet Keçeci |
| Έτος έκδοσης: | 2025 |
| Συλλογή: | VIVO: Figshare |
| Θεματικοί όροι: | Computer graphics, Graph Visualization, Hamiltonian Cycle, Z3 Theorem Prover, SMT Solver, Constraint Satisfaction Problem, CSP, Graph Theory, Graph Layout Algorithms, Keçeci Layout, Declarative Programming, Symbolic Computation, NP-Complete Problems, Computational Logic, Automated Reasoning, Data Visualization |
| Περιγραφή: | Whilst graph theory constitutes a cornerstone of computer science and mathematics education, the abstract nature of NP-complete problems, such as the Hamiltonian cycle problem, presents a significant conceptual challenge for students. An intuitive grasp of such problems often requires the analytical inspection of complex and non-standard graph structures. Traditional pedagogical methods can prove insufficient in effectively conveying this complexity, potentially diminishing student engagement. In response to these pedagogical challenges, this paper introduces a novel, integrated computational and visual tool designed for the exploration and analysis of the Hamiltonian cycle problem. The developed framework synergises two core technologies: Z3, a high-performance Satisfiability Modulo Theories (SMT) solver from Microsoft Research, and the Keçeci Layout, a novel graph layout algorithm developed by the authors, which is optimised for sequential structures. The foundation of our approach lies in reformulating the Hamiltonian cycle problem not as a search for an algorithmic solution, but as a constraint satisfaction problem. This declarative model, which defines the mathematical rules a valid cycle must obey, is submitted to the Z3 solver to automatically prove whether a given graph contains a Hamiltonian cycle. Compared to conventional trial-and-error or brute-force algorithms, this method offers a more efficient and formally verified approach, mathematically guaranteeing the correctness of the result. When Z3 finds a solution (SAT), it produces a model representing that solution; if no solution exists (UNSAT), it definitively reports the absence of a cycle. The principal educational innovation of this work, however, emerges during the visualisation of these abstract logical results. Standard graph layout algorithms, such as the Fruchterman-Reingold method, whilst often aesthetically optimised, can produce intricate and unpredictable outputs that make tracing a sequential path or cycle difficult. In contrast, our ... |
| Τύπος εγγράφου: | article in journal/newspaper |
| Γλώσσα: | unknown |
| Relation: | https://figshare.com/articles/journal_contribution/Interactive_Exploration_of_the_Hamiltonian_Problem_with_Z3_and_the_Ke_eci_Layout/29959778 |
| DOI: | 10.6084/m9.figshare.29959778.v2 |
| Διαθεσιμότητα: | https://doi.org/10.6084/m9.figshare.29959778.v2 https://figshare.com/articles/journal_contribution/Interactive_Exploration_of_the_Hamiltonian_Problem_with_Z3_and_the_Ke_eci_Layout/29959778 |
| Rights: | CC BY 4.0 |
| Αριθμός Καταχώρησης: | edsbas.BE5C50A0 |
| Βάση Δεδομένων: | BASE |
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