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The Cartographer
A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_4$-Minor
October 09, 2024 Β· Declared Dead Β· π International Symposium on Parameterized and Exact Computation
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Authors
Carla Groenland, Jesper Nederlof, Tomohiro Koana
arXiv ID
2410.06793
Category
cs.DS: Data Structures & Algorithms
Citations
0
Venue
International Symposium on Parameterized and Exact Computation
Last Checked
5 months ago
Abstract
We study a special case of the Steiner Tree problem in which the input graph does not have a minor model of a complete graph on 4 vertices for which all branch sets contain a terminal. We show that this problem can be solved in $O(n^4)$ time, where $n$ denotes the number of vertices in the input graph. This generalizes a seminal paper by Erickson et al. [Math. Oper. Res., 1987] that solves Steiner tree on planar graphs with all terminals on one face in polynomial time.
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