The Shuffling Buffer

Devillers, Olivier; Guigue, Philippe

doi:10.1142/s021819590100064x

Cited by 5 publications

(3 citation statements)

References 5 publications

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“…Devillers and Guigue [15] considered a different kind of partially randomized insertion order, for handling constructions for which the data is provided sequentially rather than all at once. Arriving data can be stored and reshuffled (randomly) in a buffer of limited size before it has to be inserted into the data structure.…”

Section: Discussionmentioning

confidence: 99%

Incremental constructions con BRIO

Amenta

Choi

Rote

2003

Proceedings of the Nineteenth Annual Symposium on Computational Geometry

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Section: Discussionmentioning

confidence: 99%

Incremental constructions con BRIO

Amenta

Choi

Rote

2003

Proceedings of the Nineteenth Annual Symposium on Computational Geometry

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“…Moreover, in real-life applications the curves are typically inserted to the arrangement in nonrandom order. This reduces the performance of the RIC algorithm, as it relies on random order of insertion, unless special procedures are followed [Devillers and Guigue 2001]. The basic idea behind the landmarks algorithm is to choose and locate points (landmarks) within the arrangement and store them in a data structure that supports nearest-neighbor search.…”

Section: Point Location With Landmarksmentioning

confidence: 99%

An experimental study of point location in planar arrangements in CGAL

Haran

Halperin

2009

ACM J. Exp. Algorithmics

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We study the performance in practice of various point-location algorithms implemented in CGAL (the Computational Geometry Algorithms Library), including a newly devised landmarks algorithm. Among the other algorithms studied are: a naïve approach, a "walk along a line" strategy, and a trapezoidal decomposition-based search structure. The current implementation addresses general arrangements of planar curves, including arrangements of nonlinear segments (e.g., conic arcs) and allows for degenerate input (for example, more than two curves intersecting in a single point or overlapping curves). The algorithms use exact geometric computation and thus result in the correct point location. In our landmarks algorithm (a.k.a. jump & walk), special points, "landmarks," are chosen in a preprocessing stage, their place in the arrangement is found, and they are inserted into a data structure that enables efficient nearest-neighbor search. Given a query point, the nearest landmark is located and a "walk" strategy is applied from the landmark to the query point. We report on various experiments with arrangements composed of line segments or conic arcs. The results indicate that compared to the other algorithms tested, the landmarks approach is the most efficient, when the overall (amortized) cost of a query is taken into account, combining both preprocessing and query time. The simplicity of the algorithm enables an almost straightforward implementation and rather easy maintenance. The generic programming implementation allows versatility both in the selected type of landmarks and in the choice of the nearest-neighbor search structure. The end result is an efficient point-location algorithm that bypasses the alternative CGAL implementations in most practical aspects.

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“…On the other hand, Amenta et al showed that the entropy may slowly decay during the RIC without penalty [1]; in other words, the insertion sequence can afford to be less and less random as the construction progresses. Devillers and Guigue introduced the shuffling buffer, which randomly permutes contiguous subsequences of the input sequence of a certain length k, and they provide trade-offs between the length k and the running time of the RIC [16].…”

Section: Introductionmentioning

confidence: 99%

Markov incremental constructions

Chazelle

Mulzer

2008

Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry

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A classic result asserts that many geometric structures can be constructed optimally by successively inserting their constituent parts in random order. These randomized incremental constructions (RICs) still work with imperfect randomness: the dynamic operations need only be "locally" random. Much attention has been given recently to inputs generated by Markov sources. These are particularly interesting to study in the framework of RICs, because Markov chains provide highly nonlocal randomness, which incapacitates virtually all known RIC technology.We generalize Mulmuley's theory of Θ-series and prove that Markov incremental constructions with bounded spectral gap are optimal within polylog factors for trapezoidal maps, segment intersections, and convex hulls in any fixed dimension. The main contribution of this work is threefold: (i) extending the theory of abstract configuration spaces to the Markov setting; (ii) proving Clarkson-Shor type bounds for this new model; (iii) applying the results to classical geometric problems. We hope that this work will pioneer a new approach to average-case analysis in computational geometry.

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The Shuffling Buffer

Cited by 5 publications

References 5 publications

Incremental constructions con BRIO

Incremental constructions con BRIO

An experimental study of point location in planar arrangements in CGAL

Markov incremental constructions

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