SIAM Journal on Computing
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
A heuristic selection strategy for lexicographic Gröner bases?
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Maintaining the minimal distance of a point set in polylogarithmic time
Discrete & Computational Geometry
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Randomized Data Structures for the Dynamic Closest-Pair Problem
SIAM Journal on Computing
On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
Data structures and algorithms for nearest neighbor search in general metric spaces
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
New techniques for some dynamic closest-point and farthest-point problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Experiments on traveling salesman heuristics
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Clustering Algorithms
Applications of Gröbner Bases in Non-linear Computational Geometry
Proceedings of the International Symposium on Trends in Computer Algebra
Practical approximation algorithms for zero- and bounded-skew trees
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A Study on the Hierarchical Data Clustering Algorithm Based on Gravity Theory
PKDD '01 Proceedings of the 5th European Conference on Principles of Data Mining and Knowledge Discovery
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Squarepants in a tree: sum of subtree clustering and hyperbolic pants decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal implementations of UPGMA and other common clustering algorithms
Information Processing Letters
Straight Skeletons of Three-Dimensional Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Squarepants in a tree: Sum of subtree clustering and hyperbolic pants decomposition
ACM Transactions on Algorithms (TALG)
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
GD'06 Proceedings of the 14th international conference on Graph drawing
Continuous monitoring of exclusive closest pairs
SSTD'07 Proceedings of the 10th international conference on Advances in spatial and temporal databases
Online discovery and maintenance of time series motifs
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Rapid computation of distance estimators from nucleotide and amino acid alignments
Proceedings of the 2011 ACM Symposium on Applied Computing
Closest pair queries with spatial constraints
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Unsupervised categorization of human motion sequences
Intelligent Data Analysis
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We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Gröbner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.