2011
DOI: 10.1007/978-3-642-22006-7_22
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Dynamic Planar Range Maxima Queries

Abstract: Abstract. We consider the dynamic two-dimensional maxima query problem. Let P be a set of n points in the plane. A point is maximal if it is not dominated by any other point in P . We describe two data structures that support the reporting of the t maximal points that dominate a given query point, and allow for insertions and deletions of points in P .In the pointer machine model we present a linear space data structure with O(log n + t) worst case query time and O(log n) worst case update time. This is the fi… Show more

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Cited by 15 publications
(18 citation statements)
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“…Early research focused on dominance and contour queries, both of which can be solved in O(log n + k) time using a structure of O(n) size, where k is the number of points reported [14,18,23,26,30]. Brodal and Tsakalidis [9] were the first to discover an optimal dynamic structure for topopen queries, which capture both dominance and contour queries as special cases. Their structure occupies O(n) space, answers queries in O(log n + k) time, and supports updates in O(log n) time.…”
Section: Previous Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Early research focused on dominance and contour queries, both of which can be solved in O(log n + k) time using a structure of O(n) size, where k is the number of points reported [14,18,23,26,30]. Brodal and Tsakalidis [9] were the first to discover an optimal dynamic structure for topopen queries, which capture both dominance and contour queries as special cases. Their structure occupies O(n) space, answers queries in O(log n + k) time, and supports updates in O(log n) time.…”
Section: Previous Resultsmentioning
confidence: 99%
“…This paper concentrates on 2D data for several reasons. First, planar range skyline reporting (i.e., our problem) is a classic topic that has been extensively studied in theory [9,14,15,18,23,24,26,30]. However, nearly all the existing results apply to internal memory (as reviewed in the next subsection), while currently there is little understanding about the characteristics of the problem in I/O environments.…”
Section: Motivation Of 2d Range Skylinementioning
confidence: 99%
“…We simplify a data structure described in [4] (and in some of the papers cited there) to obtain a simple solution for the operation mix needed in our application that yields a good basis for parallelization. We store the elements of Q in the leaves of a balanced binary search tree lexicographically sorted by increasing x, y-coordinate, and node ID, e.g., a red-black tree [12].…”
Section: B the Pareto Queue Qmentioning
confidence: 99%
“…Subsequently, process the even numbered tasks and finally the odd numbered ones. 4 Overall, the tasks can be processed in time O(T k /p + log p) plus the time needed for coordinating processors cooperating on split tasks which depends on the way these tasks are parallelized.…”
Section: Implementation Detailsmentioning
confidence: 99%
“…Previous work: The work in the skyline literature closest to our work are algorithms for computing skylines of points that lie within a rectangular query range [1,5]. Note that here the range restrictions and skyline are both defined on the same set of attributes, whereas in the range-skyline problem that we consider, they are defined on different sets of attributes (range attributes versus features).…”
Section: Introductionmentioning
confidence: 98%