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Author Eppstein, David
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2000
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data
Subject Keyword TSP ♦ Conga line data structure ♦ Matching ♦ Nearest-neighbor heuristic ♦ Quadtree
Abstract 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 $\textit{n}-object$ set, maintaining the closest pair, in $\textit{O}(\textit{n}$ $log^{2}$ $\textit{n})$ time per update and $\textit{O}(\textit{n})$ space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, $\textit{O}(\textit{n})$ 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.
ISSN 10846654
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2000-12-01
Publisher Place New York
e-ISSN 10846654
Journal Journal of Experimental Algorithmics (JEA)
Volume Number 5


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Source: ACM Digital Library