Diameter constrained Steiner tree and related problems

TL;DR

This paper presents a dynamic programming approach for the diameter constrained Steiner tree problem in directed graphs, along with reductions for related variants, advancing the understanding of these complex network design problems.

Contribution

It introduces a dynamic programming solution for directed graphs and polynomial reductions for variants with degree and size constraints, filling gaps in existing literature.

Findings

FPT algorithm for diameter constrained Steiner trees in directed graphs

Polynomial reductions among Steiner tree variants with additional constraints

Novelty of simple reductions not previously documented

Abstract

We give a dynamic programming solution to find the minimum cost of a diameter constrained Steiner tree in case of directed graphs. Then we show a simple reduction from undirected version to the directed version to realize an algorithm of similar complexity i.e, FPT in number of terminal vertices. Other natural variants of constrained Steiner trees are defined by imposing constraints on the min-degree and size of the Steiner tree and some polynomial time reductions among these problems are proven. To the best of our knowledge, these fairly simple reductions are not present in the literature prior to our work.