An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910250818338816 |
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| author | Sadovsky, A. |
| author_facet | Sadovsky, A. |
| contents | The Hamiltonian Path Problem is formulated as a continuous minimization problem on conductances assigned to an Ohmic network associated with the given graph. The objective function is a sum of two penalty terms that collectively enforce a set of conditions sufficient for a subgraph of the original graph to be a Hamiltonian path. The objective function is nonconvex. The main result (Theorem 1) shows that, provided the graph has a Hamiltonian path from $h^{start}$ to $h^{end}$, a conductance configuration is a global minimizer of the objective if and only if it corresponds to a Hamiltonian path. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24289 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem Sadovsky, A. Optimization and Control The Hamiltonian Path Problem is formulated as a continuous minimization problem on conductances assigned to an Ohmic network associated with the given graph. The objective function is a sum of two penalty terms that collectively enforce a set of conditions sufficient for a subgraph of the original graph to be a Hamiltonian path. The objective function is nonconvex. The main result (Theorem 1) shows that, provided the graph has a Hamiltonian path from $h^{start}$ to $h^{end}$, a conductance configuration is a global minimizer of the objective if and only if it corresponds to a Hamiltonian path. |
| title | An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.24289 |