The Nearest Neighbor Algorithm for Balanced and Connected k-Center Problem under Modular Distance

The k-center problem is a famous NP complete problem in combinatorial optimization. Under the traditional distance, there is a 2-approximation algorithm for the center problem, and the partition from the center satisfies the internal connectivity. However, under the modular distance, the partition obtained by the traditional center algorithm may not satisfy the internal connectivity. Therefore, this paper proposes the problem of balanced and connected center under modular distance, and designs a nearest neighbor algorithm. Finally, an example is given to prove the correctness of the algorithm.