VORONOI DIAGRAMS IN A RIVER

A new generalized Voronoi diagram is defined on the surface of a river with uniform flow; a point belongs to the territory of a site if and only if a boat starting from the site can reach the point faster than a boat starting from any other site. If the river runs slower than the boat, the Voronoi diagram has the same topological structure as the ordinary Voronoi diagram, and hence can be constructed from the ordinary Voronoi diagram by a certain transformation. If the river runs faster than the boat, on the other hand, the topological structure of the diagram becomes different from the ordinary one, but it can be constructed by the plane sweep technique. Moreover, Fortune’s plane sweep algorithm for constructing the ordinary Voronoi diagram can be interpreted as the algorithm for constructing the Voronoi diagram in a river in which the water flows at the same speed as the boat.

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VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE EUCLIDEAN PLANE

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195906001963 ◽

2006 ◽

Vol 16 (02n03) ◽

pp. 117-144 ◽

Cited By ~ 11

Author(s):

SANG WON BAE ◽

KYUNG-YONG CHWA

Keyword(s):

Voronoi Diagram ◽

Euclidean Plane ◽

Transportation Network ◽

Voronoi Diagrams ◽

The Other ◽

Constant Number ◽

Time Path ◽

The Given

This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2+ m3+ nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2+ n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space.

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A ROBUST TOPOLOGY-ORIENTED INCREMENTAL ALGORITHM FOR VORONOI DIAGRAMS

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195994000124 ◽

1994 ◽

Vol 04 (02) ◽

pp. 179-228 ◽

Cited By ~ 76

Author(s):

KOKICHI SUGIHARA ◽

MASAO IRI

Keyword(s):

Numerical Computation ◽

Voronoi Diagram ◽

Voronoi Diagrams ◽

The Other ◽

Geometric Algorithms ◽

Incremental Algorithm ◽

Single Precision ◽

Careful Choice ◽

Numerical Errors ◽

Incremental Method

The paper presents a robust algorithm for constructing Voronoi diagrams in the plane. The algorithm is based on an incremental method, but is quite new in that it is robust against numerical errors. Conventionally, geometric algorithms have been designed on the assumption that numerical errors do not take place, and hence they are not necessarily valid for real computers where numerical errors are inevitable. The algorithm to be proposed in this paper, on the other hand, is designed with the recognition that numerical errors are inevitable in real computation; i.e., in the proposed algorithm higher priority is placed on topological structures than on numerical values. As a result, the algorithm is "completely" robust in the sense that it always gives some output however poor the precision of numerical computation may be. In general, the output cannot be more than an approximation to the true Voronoi diagram which we should have got by infinite-precision computation. However, the algorithm is asymptotically correct in the sense that the output converges to the true diagram as the precision becomes higher. Moreover, careful choice of the way of numerical computation makes the algorithm stable enough; indeed the present version of the algorithm can construct in single-precision arithmetic a correct Voronoi diagram for one million generators randomly placed in the unit square in the plane.

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The L∞ Hausdorff Voronoi Diagram Revisited

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195915500089 ◽

2015 ◽

Vol 25 (02) ◽

pp. 123-141 ◽

Cited By ~ 2

Author(s):

Evanthia Papadopoulou ◽

Jinhui Xu

Keyword(s):

Data Structure ◽

Voronoi Diagram ◽

Semiconductor Industry ◽

Vlsi Design ◽

Structural Complexity ◽

Yield Prediction ◽

Critical Area ◽

Plane Sweep ◽

Sweep Algorithm ◽

Hausdorff Voronoi Diagram

We revisit the [Formula: see text] Hausdorff Voronoi diagram of clusters of points in the plane and present a simple two-pass plane sweep algorithm to construct it. This problem is motivated by applications in the semiconductor industry, in particular, critical area analysis and yield prediction in VLSI design. We show that the structural complexity of this diagram is [Formula: see text], where [Formula: see text] is the number of given clusters and [Formula: see text] is a number of specially crossing clusters, called essential. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where [Formula: see text] reflects a slight superset of essential crossings, [Formula: see text], and [Formula: see text] is the total number of crossing clusters. For non-crossing clusters ([Formula: see text]) or clusters with only a small number of crossings ([Formula: see text]) the algorithm is optimal. The latter is the case of interest in the motivating application, where [Formula: see text]. This is achieved by augmenting the wavefront data structure of the plane sweep, and a preprocessing step, based on point dominance, which is interesting in its own right.

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Voronoi Diagrams of Moving Points

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195998000187 ◽

1998 ◽

Vol 08 (03) ◽

pp. 365-379 ◽

Cited By ~ 40

Author(s):

Gerhard Albers ◽

Leonidas J. Guibas ◽

Joseph S. B. Mitchell ◽

Thomas Roos

Keyword(s):

Euclidean Space ◽

Voronoi Diagram ◽

Upper Bound ◽

Voronoi Diagrams ◽

Maximum Length ◽

The Other ◽

Dimensional Euclidean Space ◽

Moving Points ◽

Over Time

Consider a set of n points in d-dimensional Euclidean space, d ≥ 2, each of which is continuously moving along a given individual trajectory. As the points move, their Voronoi diagram changes continuously, but at certain critical instants in time, topological events occur that cause a change in the Voronoi diagram. In this paper, we present a method of maintaining the Voronoi diagram over time, at a cost of O( log n) per event, while showing that the number of topological events has an upper bound of O(ndλs(n)), where λs(n) is the (nearly linear) maximum length of a (n,s)-Davenport-Schinzel sequence, and s is a constant depending on the motions of the point sites. In addition, we show that if only k points are moving (while leaving the other n - k points fixed), there is an upper bound of O(knd-1λs(n)+(n-k)dλ s(k)) on the number of topological events.

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Actualisation du catalogue des pteridophytes du Nord Ouest Algerien (region de Tlemcen). An update of the cheklist of pteridophytes from Nordwest Algeria (Tlemcen region)

Acta Botanica Malacitana ◽

10.24310/abm.v38i0.2638 ◽

2013 ◽

Vol 38 ◽

pp. 33-39 ◽

Cited By ~ 6

Author(s):

Boumediene Medjahdi ◽

Assia Ltreuch-Belarouci ◽

Rémy Prelli

Keyword(s):

Nous Avons ◽

Genetic Resources ◽

Threatened Species ◽

The Other ◽

Natural Distribution ◽

Ecological Characteristics ◽

Statutory Protection ◽

Ouest Algérien ◽

A Site ◽

Ressources Génétiques

Français. Un inventaire des ptéridophytes a été entrepris dans les forêts de la région de Tlemcen. L’inventaire de ces populations constitue une étape importante pour le développement des stratégies de conservation des ressources génétiques et de la diversité de ces populations sur l’ensemble de leur aire de distribution naturelle. Nous avons ainsi effectué le recensement et l’identification des fougères existantes dans la région de Tlemcen. Au total, plusieurs stations dont les caractéristiques écologiques diffèrent d’un site à un autre ont été prospectées, cela a permis l’identification de 26 taxons (dont 5 exceptionnellement rare). La création de réserves naturelles forestières renforcée par une protection réglementaire des espèces les plus menacées est nécessaire pour le maintien de ces communautés si particulières. English. An inventory of Pteridophyta was begun in the forests of the Tlemcen region. The inventory of these populations constitutes an important stage for the developement of the strategies of preservation of the genetic resources and the diversity of these populations on their whole area of natural distribution. We so made the inventory and the identification of the existing ferns in the region of Tlemcen. On the whole, several stations the ecological characteristics differ from a site in the other one were canvassed; they allowed the identification of 26 taxes (among which 5 exceptionally rare). The creation of forest nature reserves strengthened by a statutory protection of the most threatened species is necessary for the preservation of these particular communities.

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In-Memory Interval Joins

The VLDB Journal ◽

10.1007/s00778-020-00639-0 ◽

2021 ◽

Author(s):

Panagiotis Bouros ◽

Nikos Mamoulis ◽

Dimitrios Tsitsigkos ◽

Manolis Terrovitis

Keyword(s):

Parallel Computation ◽

State Of The Art ◽

Complex Data ◽

Plane Sweep ◽

Join Algorithm ◽

Sweep Algorithm ◽

Join Algorithms ◽

Domain Partitioning ◽

Complex Data Structure ◽

Independent Tasks

AbstractThe interval join is a popular operation in temporal, spatial, and uncertain databases. The majority of interval join algorithms assume that input data reside on disk and so, their focus is to minimize the I/O accesses. Recently, an in-memory approach based on plane sweep (PS) for modern hardware was proposed which greatly outperforms previous work. However, this approach relies on a complex data structure and its parallelization has not been adequately studied. In this article, we investigate in-memory interval joins in two directions. First, we explore the applicability of a largely ignored forward scan (FS)-based plane sweep algorithm, for single-threaded join evaluation. We propose four optimizations for FS that greatly reduce its cost, making it competitive or even faster than the state-of-the-art. Second, we study in depth the parallel computation of interval joins. We design a non-partitioning-based approach that determines independent tasks of the join algorithm to run in parallel. Then, we address the drawbacks of the previously proposed hash-based partitioning and suggest a domain-based partitioning approach that does not produce duplicate results. Within our approach, we propose a novel breakdown of the partition-joins into mini-joins to be scheduled in the available CPU threads and propose an adaptive domain partitioning, aiming at load balancing. We also investigate how the partitioning phase can benefit from modern parallel hardware. Our thorough experimental analysis demonstrates the advantage of our novel partitioning-based approach for parallel computation.

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Fast CORDIC based Generalized-Voronoi-Diagram Hardware Accelerator for Efficient Robotic Exploration

2020 5th International Conference on Robotics and Automation Engineering (ICRAE) ◽

10.1109/icrae50850.2020.9310864 ◽

2020 ◽

Author(s):

Yi Zhan ◽

Zihao Wang ◽

Jiarui Xu ◽

Guoyi Yu ◽

Fengwei An ◽

...

Keyword(s):

Voronoi Diagram ◽

Hardware Accelerator ◽

Robotic Exploration ◽

Generalized Voronoi Diagram

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β-Li0.37Na0.63Fe(MoO4)2

Acta Crystallographica Section E Structure Reports Online ◽

10.1107/s1600536814000646 ◽

2014 ◽

Vol 70 (2) ◽

pp. i9-i10 ◽

Cited By ~ 6

Author(s):

Amira Souilem ◽

Mohamed Faouzi Zid ◽

Ahmed Driss

Keyword(s):

Crystal Structure ◽

Solid State ◽

Solid State Reaction ◽

Title Compound ◽

General Position ◽

Site Occupancy ◽

The Other ◽

Main Structure ◽

Axis Direction ◽

A Site

The title compound, lithium/sodium iron(III) bis[orthomolybdate(VI)], was obtained by a solid-state reaction. The main structure units are an FeO6octahedron, a distorted MoO6octahedron and an MoO4tetrahedron sharing corners. The crystal structure is composed of infinite double MoFeO11chains along theb-axis direction linked by corner-sharing to MoO4tetrahedra so as to form Fe2Mo3O19ribbons. The cohesion between ribbonsviamixed Mo—O—Fe bridges leads to layers arranged parallel to thebcplane. Adjacent layers are linked by corners shared between MoO4tetrahedra of one layer and FeO6octahedra of the other layer. The Na+and Li+ions partially occupy the same general position, with a site-occupancy ratio of 0.631 (9):0.369 (1). A comparison is made withAFe(MoO4)2(A= Li, Na, K and Cs) structures.

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