A Structural Equivalence of Symmetric TSP to a Constrained Group Steiner Tree Problem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914308174118912 |
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| author | Arslanoğlu, Yılmaz |
| author_facet | Arslanoğlu, Yılmaz |
| contents | We present a brief structural equivalence between the symmetric TSP and a constrained Group Steiner Tree Problem (cGSTP) defined on a simplicial incidence graph. Given the complete weighted graph on the city set V, we form the bipartite incidence graph between triangles and edges. Selecting an admissible, disk-like set of triangles induces a unique boundary cycle. With global connectivity and local regularity constraints, maximizing net weight in the cGSTP is exactly equivalent to minimizing the TSP tour length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Structural Equivalence of Symmetric TSP to a Constrained Group Steiner Tree Problem Arslanoğlu, Yılmaz Data Structures and Algorithms Discrete Mathematics Combinatorics Geometric Topology We present a brief structural equivalence between the symmetric TSP and a constrained Group Steiner Tree Problem (cGSTP) defined on a simplicial incidence graph. Given the complete weighted graph on the city set V, we form the bipartite incidence graph between triangles and edges. Selecting an admissible, disk-like set of triangles induces a unique boundary cycle. With global connectivity and local regularity constraints, maximizing net weight in the cGSTP is exactly equivalent to minimizing the TSP tour length. |
| title | A Structural Equivalence of Symmetric TSP to a Constrained Group Steiner Tree Problem |
| topic | Data Structures and Algorithms Discrete Mathematics Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2602.05773 |