# On balanced clustering with tree-like structures over clusters

## TL;DR

This paper introduces new greedy algorithms for balanced clustering with tree-like structures, useful in network design and routing, and provides detailed strategies and an illustrative example.

## Contribution

It proposes four novel greedy-like strategies for balanced clustering with tree structures, including an extended spanning-balancing approach and detailed implementation schemes.

## Key findings

- Extended description of spanning-balancing strategy
- Four solving schemes for the strategies
- Illustrative numerical example demonstrating effectiveness

## Abstract

The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design, management and routing). Various types of the initial elements are considered. Four basic greedy-like solving strategies (design framework) are considered: balancing-spanning strategy, spanning-balancing strategy, direct strategy, and design of layered structures with balancing. An extended description of the spanning-balancing strategy is presented including four solving schemes and an illustrative numerical example.