Randomized Data Structures for the Dynamic Closest-Pair Problem
نویسندگان
چکیده
منابع مشابه
A 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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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.
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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...
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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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Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point mi ∈ M with an independent probability pi. How difficult is it to compute elementary statistics about the closest pair of points in such a subset? For instance, what is the probability that the distance between the closest pair of points in the random subset is no more ...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1998
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539794277718