# Linear algorithms on Steiner domination of trees

## TL;DR

This paper introduces a linear-time algorithm for finding the minimum Steiner dominating set in trees, advancing the efficiency of solving this graph domination problem.

## Contribution

It presents the first linear algorithm specifically designed for computing the Steiner domination number in trees, improving computational efficiency.

## Key findings

- The algorithm computes minimum Steiner dominating sets in linear time.
- It demonstrates improved efficiency over previous methods.
- The approach is applicable to various tree structures.

## Abstract

A set of vertices $W$ in a connected graph $G$ is called a Steiner dominating set if $W$ is both Steiner and dominating set. The Steiner domination number $\gamma_{st}(G)$ is the minimum cardinality of a Steiner dominating set of $G$. A linear algorithm is proposed in this paper for finding a minimum Steiner dominating set for a tree $T$.