Three partition refinement algorithms
SIAM Journal on Computing
Algorithms for clustering data
Algorithms for clustering data
Partitioning arrangements of lines, part II: applications
Discrete & Computational Geometry
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Optimal Partitioning for Classification and Regression Trees
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithms for subset testing and finding maximal sets
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Probing polygons minimally is hard
Computational Geometry: Theory and Applications
Randomized algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Geometric decision trees for optical character recognition (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing Many Faces in Arrangements of Lines and Segments
SIAM Journal on Computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Lower bounds for set intersection queries
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Representing sets with constant time equality testing
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
Introduction to Algorithms
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On the Complexity of Shattering Using Arrangements
On the Complexity of Shattering Using Arrangements
A note on data structures for maintaining bipartitions
Journal of Discrete Algorithms
Counting and computing the Rand and block distances of pairs of set partitions
Journal of Discrete Algorithms
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Efficiently maintaining the partition induced by a set of features is an important problem in building decision-tree classifiers. In order to identify a small set of discriminating features, we need the capability of efficiently adding and removing specific features and determining the effect of these changes on the induced classification or partition. In this paper we introduce a variety of randomized and deterministic data structures to support these operations on both general and geometrically induced set partitions. We give both Monte Carlo and Las Vegas data structures that realize near-optimal time bounds and are practical to implement. We then provide a faster solution to this problem in the geometric setting. Finally, we present a data structure that efficiently estimates the number of partitions separating elements.