An Efficient Data Structure for Dynamic Closest Pair Problem
نویسندگان
چکیده
منابع مشابه
Efficient Algorithms for the Closest Pair Problem and Applications
The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed radius nearest neighbors problem (FRNNP). Given a set of points and a radius R, the problem is, for every input point p, to identify all the other input points...
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A closer look is taken at the well-known divide-andconquer algorithm for finding the closest pair of a set of points in the plane under the Euclidean distance. An argument is made that it is sufficient, and sometimes necessary, to check only the next three points following the current point associated with the y-sorted array in the combine phase of the algorithm.
متن کاملAn Optimal Algorithm for Closest-Pair Maintenance
Given a set S of n points in k-dimensional space, and an L t metric, the dynamic closest pair problem is deened as follows: nd a closest pair of S after each update of S (the insertion or the deletion of a point). For xed dimension k and xed metric L t , we give a data structure of size O(n) that maintains a closest pair of S in O(log n) time per insertion and deletion. The running time of algo...
متن کاملEfficient Randomized Incremental Algorithm For The Closest Pair Problem Using Leafary Trees
1. O(n) expected time randomized algorithms are presented in [4, 5, 7]. They use hashing and assumes the floor function as a unit cost operation. 2. An O(n log log n) time deterministic algorithm is presented in [3] which uses hashing and assumes floor function as a unit cost operation. 3. In [1] an O(n) expected time randomized algorithm using the real-RAM model is presented. This algorithm as...
متن کاملA Reliable Randomized Algorithm for the Closest-Pair Problem
The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set {0, . . . , U − 1}. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where ...
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ژورنال
عنوان ژورنال: Energy Procedia
سال: 2011
ISSN: 1876-6102
DOI: 10.1016/j.egypro.2011.12.168