Agglomerative Clustering of Growing Squares

by   Thom Castermans, et al.
Aarhus Universitet
TU Eindhoven

We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of n disjoint growing squares. Our data structure uses O(n ( n n)^2) space, supports queries in worst case O(^3 n) time, and updates in O(^7 n) amortized time. This leads to an O(nα(n)^7 n) time algorithm to solve the agglomerative clustering problem. This is a significant improvement over the current best O(n^2) time algorithms.


page 1

page 2

page 3

page 4


Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles

In this paper we study two geometric data structure problems in the spec...

Fully dynamic hierarchical diameter k-clustering and k-center

We develop dynamic data structures for maintaining a hierarchical k-cent...

(1-ε)-approximate fully dynamic densest subgraph: linear space and faster update time

We consider the problem of maintaining a (1-ϵ)-approximation to the dens...

Point Location in Incremental Planar Subdivisions

We study the point location problem in incremental (possibly disconnecte...

Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees

We study the problem of designing a resilient data structure maintaining...

Modern hierarchical, agglomerative clustering algorithms

This paper presents algorithms for hierarchical, agglomerative clusterin...

A Proposal of Interactive Growing Hierarchical SOM

Self Organizing Map is trained using unsupervised learning to produce a ...

Please sign up or login with your details

Forgot password? Click here to reset