Algorithms for three-dimensional dominance searching in linear space

Makris, Christos; Tsakalidis, Athanasios K.

doi:10.1016/s0020-0190(98)00075-1

Cited by 31 publications

(31 citation statements)

References 11 publications

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“…We close this chapter with the note that a method almost identical to the one described here for three dimensional domination searches is also described in [28] as the later reference search showed.…”

Section: Searching In Higher Dimensionsmentioning

confidence: 89%

Orthogonal Range Searching

Tiwary¹,

Seidel²

2008

Computational Geometry

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Section: Searching In Higher Dimensionsmentioning

confidence: 89%

Orthogonal Range Searching

Tiwary¹,

Seidel²

2008

Computational Geometry

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“…It is clear that we can ignore the fourth coordinate of all the points since all the points in M have their fourth coordinate larger than any points in T i so in the rest of the proof we assume M and T i are in the three dimensional space (or equivalently, we use M and T i to refer to their projection onto the first three dimensions). Using a classical idea [19], the problem can in fact be turned to an offline point location problem:…”

Section: Offline Point Locationmentioning

confidence: 99%

Fast Computation of Output-Sensitive Maxima in a Word RAM

Afshani¹

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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In this paper, we study the problem of computing the maxima of a set of n points in three dimensions with integer coordinates and show that in a word RAM, the maxima can be found in O n log log n/h n deterministic time in which h is the output size. For h = n 1−α this is O(n log(1/α)). This improves the previous O(n log log h) time algorithm and can be considered surprising since it gives a linear time algorithm when α > 0 is a constant, which is faster than the current best deterministic and randomized integer sorting algorithms. We observe that improving this running time is most likely difficult since it requires breaking a number of important barriers, even if randomization is allowed.Additionally, we show that the same deterministic running time could be achieved for performing n point location queries in an arrangement of size h. Finally, our maxima result can be extended to higher dimensions by paying a log n/h n factor penalty per dimension. This has further interesting consequences for example it preserves the linear running time when h ≤ n 1−α , for a constant α > 0, and thus it shows that for a variety of input distributions the maxima can be computed in linear expected time without knowing the distribution.

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“…In spite of the existence of an extensive literature, only a limited number of special orthogonal range search problems admit linear space data structures with polylogarithmic query time solutions. These special problems include the three-sided 2-D range queries 17] and the 3-D dominance queries 6,15]. Otherwise, all fast query algorithms require nonlinear space, sometimes coupled with matching lower bounds under certain computational models 4,5,12].…”

Section: Previous Related Workmentioning

confidence: 99%

Techniques for Indexing and Querying Temporal Observations for a Collection of Objects

Shi

JáJá

2004

Algorithms and Computation

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We consider the problem of dynamically indexing temporal observations about a collection of objects, each observation consisting of a key identifying the object, a list of attribute values and a timestamp indicating the time at which these values were recorded. We m a k e no assumptions about the rates at which these observations are collected, nor do we assume that the various objects have about the same number of observations. We d e v elop indexing structures that are almost linear in the total number of observations available at any g i v en time instant, and that support dynamic insertions in polylogarithmic time. Moreover, these structures allow the quick handling of queries to identify objects whose attribute values fall within a certain range at every time instance of a speci ed time interval. Provably good bounds are established.

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Algorithms for three-dimensional dominance searching in linear space

Cited by 31 publications

References 11 publications

Orthogonal Range Searching

Orthogonal Range Searching

Fast Computation of Output-Sensitive Maxima in a Word RAM

Techniques for Indexing and Querying Temporal Observations for a Collection of Objects

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