Maintaining maxima under boundary updates

d’Amore, Fabrizio; Franciosa, Paolo Giulio; Giaccio, Roberto; Talamo, Maurizio

doi:10.1007/3-540-62592-5_64

Cited by 4 publications

(6 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 In the pointer machine linear space dynamic data structures have been presented that support reporting all maximal points. They achieve O(m) worst case [8,9,3,13] or amortized [15] query time. They support deciding whether a given query point lies above or below the staircase (maxima emptiness query) in O(log n) [8,9,15] or O(log m) [3,13] worst case time.…”

Section: Previous Resultsmentioning

confidence: 99%

“…They achieve O(m) worst case [8,9,3,13] or amortized [15] query time. They support deciding whether a given query point lies above or below the staircase (maxima emptiness query) in O(log n) [8,9,15] or O(log m) [3,13] worst case time. Maxima contour queries are supported by the structures of [3] and [9] in O(log n + t) worst case time, where t is size of the output.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Frederickson and Rodger [8], and independently Janardan [9], improve only the worst case insertion time to O(log n), preserving the other complexities. D'Amore et al [13] improve both the insertion and deletion time to O(log n) worst case, under the assumption that the updated point has the maximum or minimum x-coordinate among the points in the set (boundary updates). Kapoor [15] shows how to support both the insertion and deletion of an arbitrary point in O(log n) worst case time.…”

Section: Previous Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Planar Range Maxima Queries

Brodal

Tsakalidis

2011

Automata, Languages and Programming

View full text Add to dashboard Cite

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 first dynamic data structure for the planar maxima dominance query problem that achieves these bounds in the worst case. The data structure also supports the more general query of reporting the maximal points among the points that lie in a given 3-sided orthogonal range unbounded from above in the same complexity. We can support 4-sided queries in O(log 2 n + t) worst case time, and O(log 2 n) worst case update time, using O(n log n) space, where t is the size of the output. This improves the worst case deletion time of the dynamic rectangular visibility query problem from O(log 3 n) to O(log 2 n). We adapt the data structure to the RAM model with word size w, where the coordinates of the points are integers in the range U ={0, . . . , 2 w −1}. We present a linear space data structure that supports 3-sided range maxima queries in O( log n log log n +t) worst case time and updates in O( log n log log n ) worst case time. These are the first sublogarithmic worst case bounds for all operations in the RAM model.

show abstract

Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Planar Range Maxima Queries

Brodal

Tsakalidis

2011

Automata, Languages and Programming

View full text Add to dashboard Cite

show abstract

“…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%

I/O-efficient planar range skyline and attrition priority queues

Kejlberg-Rasmussen

Tao

Tsakalidis

et al. 2013

Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

View full text Add to dashboard Cite

We study the static and dynamic planar range skyline reporting problem in the external memory model with block size B, under a linear space budget. The problem asks for an O(n/B) space data structure that stores n points in the plane, and supports reporting the k maximal input points (a.k.a. skyline) among the points that lie within a givenone of its edges is grounded, two variants arise: topopen for β2 = ∞ and left-open for α1 = −∞ (symmetrically bottom-open and right-open) queries.We present optimal static data structures for top-open queries, for the cases where the universe is R 2 , a U × U grid, and rank space [O(n)] 2 . We also show that left-open queries are harder, as they require Ω((n/B) + k/B) I/Os for > 0, when only linear space is allowed. We show that the lower bound is tight, by a structure that supports 4-sided queries in matching complexities. Interestingly, these lower and upper bounds coincide with those of the planar orthogonal range reporting problem, i.e., the skyline requirement does not alter the problem difficulty at all! Finally, we present the first dynamic linear space data structure that supports top-open queries in O(log 2B n + k/B 1− ) and updates in O(log 2B n) worst case I/Os, for ∈ [0, 1]. This also yields a linear space data structure for 4-sided queries with optimal query I/Os and O(log(n/B)) amortized update I/Os. We consider of independent interest the main component of our dynamic structures, a new realtime I/O-efficient and catenable variant of the fundamental structure priority queue with attrition by Sundar. * The full version is found on http://arxiv.org under the same title.

show abstract

“…Surprisingly, not much research work has been carried out while explicitly considering this setting (some steps in this direction are moved in Ref. [9]). …”

Section: Applicationsmentioning

confidence: 99%

Intersection Problems on Segments Under Boundary Updates With Application to Persistent Lists

d’Amore

Giaccio

1999

Int. J. Comput. Geom. Appl.

Self Cite

View full text Add to dashboard Cite

We consider some intersection problems on segments of H 2 in the partially dynamic setting called boundary update, where updates occur at the boundary of a given region. In particular, we maintain a set S of line segments under (boundary) insertions and deletions, such that, given a line segment t either of fixed slope or originating from a fixed point and given a point p € S D £, we can efficiently and orderly report all segments intersecting £; insertions/deletions of segments occur at the boundaries of a vertical infinite slab. We provide practical algorithms requiring C?(|

show abstract

Maintaining maxima under boundary updates

Cited by 4 publications

References 7 publications

Dynamic Planar Range Maxima Queries

Dynamic Planar Range Maxima Queries

I/O-efficient planar range skyline and attrition priority queues

Intersection Problems on Segments Under Boundary Updates With Application to Persistent Lists

Contact Info

Product

Resources

About