Network design: Improves approximation algorithms for problems like the Group Steiner tree problem (a generalization of the Steiner tree problem) and Buy-at-bulk network design (a problem in Network planning and design) by simplifying the metric space to a tree metric. Clustering: Enhances algorithms for clustering problems where hierarchical clustering can be performed more efficiently on tree metrics. Online algorithms: Benefits problems like the k-server problem and metrical task system by providing better competitive ratios through simplified metrics.
Network design Improves approximation algorithms for problems like the Group Steiner tree problem (a generalization of the Steiner tree problem) and Buy-at-bulk network design (a problem in Network planning and design) by simplifying the metric space to a tree metric Clustering Enhances algorithms for clustering problems where hierarchical clustering can be performed more efficiently on tree metrics Online algorithms Benefits problems like the k-server problem and metrical task system by providing better competitive ratios through simplified metrics