Uncertain Voronoi diagram

Jooyandeh, Mohammadreza; Mohades, Ali; Mirzakhah, Maryam

doi:10.1016/j.ipl.2009.03.007

Cited by 39 publications

(17 citation statements)

References 2 publications

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“…All of these methods were based on heuristics and did not provide any guarantee on the query time in the worst case. Moreover, recent results that rely on Voronoi diagram for supporting nearest neighbor queries under uncertainty cannot be adapted to answer ENN (see [13,21,33]). We are not aware of any index that uses near-linear space and returns in sublinear time the expected nearest neighbor or a point that is the most likely nearest neighbor.…”

Section: Previous Resultsmentioning

confidence: 99%

Nearest-neighbor searching under uncertainty

Agarwal

Aronov

Har-Peled

et al. 2012

Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor (ENN). We present methods for computing an exact ENN or an ε-approximate ENN, for a given error parameter 0 < ε < 1, under different distance functions. These methods build an index of near-linear size and answer ENN queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or ε-approximate ENN queries with provable performance guarantees.

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Section: Previous Resultsmentioning

confidence: 99%

Nearest-neighbor searching under uncertainty

Agarwal

Aronov

Har-Peled

et al. 2012

Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…In reality, the number of existing graph energies may be still greater, and more such will for sure appear in the future. 1) (ordinary) graph energy [12] 2) extended adjacency energy [30] 3) Laplacian energy [36] 4) energy of matrix [41] 5) minimum robust domination energy [49] 6) energy of set of vertices [50] 7) distance energy [37] 8) Laplacian-energy-like invariant [51] 9) Consonni-Todeschini energies [40] 10) energy of (0,1)-matrix [52] 11) incidence energy [53] 12) maximum-degree energy [54] 13) skew Laplacian energy [55] 14) oriented incidence energy [56] 15) skew energy [57] 16) Randić energy [39] 17) normalized Laplacian energy [38] 18) energy of matroid [58] 19) energy of polynomial [42] 20) Harary energy [59] 21) sum-connectivity energy [60] 22) second-stage energy [61] 23) signless Laplacian energy [62] 24) PI energy [63] 25) Szeged energy [64] 26) He energy [65] 27) energy of orthogonal matrix [66] 28) common-neighborhood energy [67] 29) matching energy [43] 30) Seidel energy [68] 31) ultimate energy [69] 32) minimum-covering energy [70] 33) resistance-distance energy [71] 34) Kirchhoff energy [72] 35) color energy [73] 36) normalized incidence energy [74] 37) Laplacian distance energy [75] 38) Laplacian incidence energy [76] 39) Laplacian minimum dominating energy …”

Section: The Graph Energy Delugementioning

confidence: 99%

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

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Abstract:The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing.We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic.

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“…In [21,37], the Voronoi diagram was modified to identify an imprecise object that is surely the nearest object of a query point q. However, the UV-diagram returns object(s) that may have chance to be the nearest neighbor of q, and can be used to answer probabilistic nearest-neighbor queries.…”

Section: Related Workmentioning

confidence: 99%

UV-diagram: a voronoi diagram for uncertain spatial databases

et al. 2012

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The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the Uncertain-Voronoi diagram (or UV-diagram), which divides the data space into disjoint "UV-partitions". Each UV-partition P is associated with a set S of objects, such that any point q located in P has the set S as its nearest neighbor with nonzero probabilities. The UV-diagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point q. It supports "continuous nearest-neighbor search", which refreshes the set of NN objects of q, as the position of q changes. It also allows the analysis of nearestneighbor information, for example, to find out the number of objects that are the nearest neighbors of any point in a given area. A UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation of a UV-diagram, by using a set of UV-cells. A UV-cell of an object o is the extent e for which o can be the nearest neighbor of any point q ∈ e. We study how to speed up the derivation of UV-cells by considering its nearby objects. We also use the UV-cells to design the UV-index, which supports different queries, and can be constructed in polynomial time. We have performed extensive experiments on both real and synthetic data to validate the efficiency of our approaches.

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Uncertain Voronoi diagram

Cited by 39 publications

References 2 publications

Nearest-neighbor searching under uncertainty

Nearest-neighbor searching under uncertainty

The Total π-Electron Energy Saga

UV-diagram: a voronoi diagram for uncertain spatial databases

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