An Analysis of Random d-Dimensional Quad Trees
نویسندگان
چکیده
It is shown that the depth of the last node inserted in a random quad tree constructed from independent uniform [Q, 11d random vectors is in probability asymptotic to (2/d) log n, where log denotes the natural logarithm. In addition, for d =2, exact values are obtained for all the moments of the depth of the last node .
منابع مشابه
P´olya Urn Models and Connections to Random Trees: A Review
This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...
متن کاملOn the internal path length of d-dimensional quad trees
It is proved that the internal path length of a d–dimensional quad tree after normalization converges in distribution. The limiting distribution is characterized as a fixed point of a random affine operator. We obtain convergence of all moments and of the Laplace transforms. The moments of the limiting distribution can be evaluated from the recursion and lead to first order asymptotics for the ...
متن کاملIsing models and multiresolution quad - trees by
We study percolation and Ising models defined on generalizations of quad-trees used in multiresolution image analysis. These can be viewed as trees for which each mother vertex has 2 daughter vertices, and for which daughter vertices are linked together in d-dimensional Euclidean configurations. Retention probabilities / interaction strengths differ according to whether the relevant bond is bet...
متن کاملPartial Match Queries in Relaxed K-dt trees
The study of partial match queries on random hierarchical multidimensional data structures dates back to Ph. Flajolet and C. Puech’s 1986 seminal paper on partial match retrieval. It was not until recently that fixed (as opposed to random) partial match queries were studied for random relaxed K-d trees, random standard K-d trees, and random 2-dimensional quad trees. Based on those results it se...
متن کاملEntropy Quad-Trees for High Complexity Regions Detection
This paper introduces entropy quad-trees, which are structures derived from quad-trees by allowing nodes to split only when those correspond to sufficiently complex sub-domains of a data domain. Complexity is evaluated using an information-theoretic measure based on the analysis of the entropy associated to sets of objects designated by nodes. An alternative measure related to the concept of bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Comput.
دوره 19 شماره
صفحات -
تاریخ انتشار 1990