Minimum Connected Dominating Set Based on Minimum Spanning Tree

In this article, we present an optimized algorithm for finding minimum connected dominating sets based on minimum spanning trees. This algorithm effectively solves network planning problems similar to establishing new broadcast towers in a city where every resident must receive broadcast signals. The implementation typically involves constructing a minimum spanning tree (using algorithms like Prim's or Kruskal's) and then applying domination set reduction techniques. We will demonstrate through detailed examples how this MST-based algorithm solves such problems, including code implementation approaches like adjacency matrix processing and greedy selection strategies. Additionally, we will discuss the algorithm's advantages in terms of time complexity (often O(E log V) for MST construction) and limitations regarding dynamic network topologies. The article will also explore applications to similar problems such as wireless sensor network design and infrastructure optimization, where connectivity and minimal resource allocation are crucial.