A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_4$-Minor

Carla Groenland; Jesper Nederlof; Tomohiro Koana

paper

A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_{4}$ -Minor

arXiv:2410.06793

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.

A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a K4​-Minor

Abstract

A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_{4}$ -Minor