On Dasgupta’s Hierarchical Clustering Objective and Its Relation to Other Graph Parameters
Journal article, Peer reviewed
Accepted version
![Thumbnail](/bora-xmlui/bitstream/handle/11250/2982359/Hierarchical_clusterings_of_trees.pdf.jpg?sequence=5&isAllowed=y)
View/ Open
Date
2021Metadata
Show full item recordCollections
- Department of Informatics [978]
- Registrations from Cristin [10237]
Original version
Lecture Notes in Computer Science (LNCS). 2021, 12867, 287-300. 10.1007/978-3-030-86593-1_20Abstract
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees. Motivated by a correspondence with Dasgupta’s objective for hierarchical clustering we consider the total rather than maximum depth of vertices as an alternative objective for minimization. For vertex partition trees this leads to a new parameter with a natural interpretation as a measure of robustness against vertex removal. As tools for the study of this family of parameters we show that they have similar recursive expressions and prove a binary tree rotation lemma. The new parameter is related to trivially perfect graph completion and therefore intractable like the other three are known to be. We give polynomial-time algorithms for both total-depth variants on caterpillars and on trees with a bounded number of leaf neighbors. For general trees, we obtain a 2-approximation algorithm.