Limit distribution of the number of consecutive records
Random Structures & Algorithms
Phase changes in random point quadtrees
ACM Transactions on Algorithms (TALG)
Rank selection in multidimensional data
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We solve the open problem of characterizing the leading constant in the asymptotic approximation to the expected cost used for random partial match queries in random k-d trees. Our approach is new and of some generality; in particular, it is applicable to many problems involving differential equations (or difference equations) with polynomial coefficients.