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Property Testing with Geometric Queries [chapter]

Artur Czumaj, Christian Sohler
2001 Lecture Notes in Computer Science  
Although there has been some research previously done in testing geometric properties, prior works have been mostly dealing with the study of combinatorial notion of the distance defining whether an object  ...  This paper investigates geometric problems in the context of property testing algorithms.  ...  Tester for convexity for the Hamming distance using geometric queries In the previous sections we discussed testing convexity properties in geometric setting.  ... 
doi:10.1007/3-540-44676-1_22 fatcat:aiq22mqiafak7frjykwwveq7iy

Geometric Querying for Dynamic Exploration of Multidimensional Data [chapter]

Olga Sourina
2003 Lecture Notes in Computer Science  
The queries are formulated with geometric objects and operations over them. The geometric objects and operations are described with implicit functions.  ...  Data from database are interpreted geometrically as multidimensional points. A query window is a query solid of any shape specified by its location.  ...  To retrieve materials with the properties of ultimate strength, yield strength and test temperature located no further than a 1 , b 1 , c 1 distances from the material with properties values (x 1 , y 1  ... 
doi:10.1007/3-540-44843-8_46 fatcat:nxla3pthcjaelkt5ci3hohukh4

Spatial operators

Eliseo Clementini, Paolino Di Felice
2000 SIGMOD record  
A taxonomy of requirements to be satis ed by spatial operators is proposed with emphasis on users' needs and on the introduction of data uncertainty s u p p o r t .  ...  This paper discusses issues related to the integration of spatial operators into the new generation of SQL-like query languages.  ...  Similarity criteria may i n volve geometric aspects of the objects (such as shape or topological properties).  ... 
doi:10.1145/362084.362101 fatcat:vfy3fqwd2bgw7aojbgqg6xjkhi

Geometric query types for data retrieval in relational databases

Olga Sourina, Seng H. Boey
1998 Data & Knowledge Engineering  
The spatial queries are formulated with geometric objects and operations over them. Descriptions of geometric objects and operations with implicit functions are proposed.  ...  Our aim is to propose a query model that will provide the user of scientific and engineering databases with geometric query tools.  ...  Query 4 . 4 Retrieve long-term strength property values under the condition of the test temperature tjand test time l I for some material.  ... 
doi:10.1016/s0169-023x(97)00061-x fatcat:k6mgwmzdkvf2jjjj5vfjm7ujwu

Testing Euclidean Spanners [chapter]

Frank Hellweg, Melanie Schmidt, Christian Sohler
2010 Lecture Notes in Computer Science  
In this paper we develop a property testing algorithm for the problem of testing whether a directed geometric graph with bounded (out)degree is a (1 + δ)-spanner.  ...  In this paper, we show that the property of being a (1 + δ)-spanner can be tested with O δ −3d −3 √ n queries for bounded (out)degree graphs.  ...  In this paper we continue the study of property testing algorithms for geometric properties.  ... 
doi:10.1007/978-3-642-16367-8_24 fatcat:iqsbswappnfjfe42hdr7wbbpmu

Testing Euclidean Spanners [chapter]

Frank Hellweg, Melanie Schmidt, Christian Sohler
2010 Lecture Notes in Computer Science  
In this paper we develop a property testing algorithm for the problem of testing whether a directed geometric graph with bounded (out)degree is a (1 + δ)-spanner.  ...  In this paper, we show that the property of being a (1 + δ)-spanner can be tested with O δ −3d −3 √ n queries for bounded (out)degree graphs.  ...  In this paper we continue the study of property testing algorithms for geometric properties.  ... 
doi:10.1007/978-3-642-15775-2_6 fatcat:od5soljuxnabvpmvr3y2acessi

Property Testing in Computational Geometry [chapter]

Artur Czumaj, Christian Sohler, Martin Ziegler
2000 Lecture Notes in Computer Science  
We show that many basic geometric properties have very efficient testing algorithms, whose running time is significantly smaller than the object description size.  ...  We consider the notion of property testing as applied to computational geometry.  ...  In this work we consider property testing as applied to geometric objects in Euclidean spaces.  ... 
doi:10.1007/3-540-45253-2_15 fatcat:fn2bvhtfjbcmtl7stflqrqy7zu

Testing Euclidean minimum spanning trees in the plane

Artur Czumaj, Christian Sohler
2008 ACM Transactions on Algorithms  
These algorithms are designed in a similar flavor as that in property testing.  ...  We present a property testing algorithm that accepts graph G if it is an EMST of P and that rejects with probability at least 2 3 if G differs from every EMST of P in more than ǫ n edges.  ...  The query complexity measures the number of queries to the oracle asked by a property testing algorithm.  ... 
doi:10.1145/1367064.1367071 fatcat:jwaxm33yw5bs7bmn4ugwsptvki

From 3d geomodelling systems towards 3d geoscience information systems: Data model, query functionality, and data management

Marcus Apel
2006 Computers & Geosciences  
observation data and 3d geomodels based on their 3d spatial and geological properties.  ...  The resulting 3d GIS framework enables geologists to manipulate, analyse and interpret 3d geomodels analogously as they work with 2d geological maps. r  ...  distance of a given geoobject.'' (2) Property queries, which return a geometrical or metrical property. (3) Orientation queries, for example: ''Select the set of faults with a given normal orientation  ... 
doi:10.1016/j.cageo.2005.06.016 fatcat:bpa2auvgivbftf6dh56xgfnsli

A Theory-Based Evaluation of Nearest Neighbor Models Put Into Practice [article]

Hendrik Fichtenberger, Dennis Rohde
2018 arXiv   pre-print
We develop a randomized algorithm with one-sided error that decides this question, i.e., a property tester for the k-NN property, with complexity O(√(n) k^2 / ϵ^2) measured in terms of the number of vertices  ...  We study property testing of k-NN graphs in theory and evaluate it empirically: given a point set P ⊂R^δ and a directed graph G=(P,E), is G a k-NN graph, i.e., every point p ∈ P has outgoing edges to its  ...  In this paper, we consider property testing on directed geometric graphs with bounded average degree d. Definition 1 (geometric graph).  ... 
arXiv:1810.05064v3 fatcat:wwps6i7qjnhmhgczau4ai5asty

Fast Statistically Geometric Reasoning About Uncertain Line Segments in 2D- and 3D-Space [chapter]

Christian Beder
2004 Lecture Notes in Computer Science  
In the first part a framework is presented, that allows to represent uncertain line segments in 2D-and 3D-space and perform statistical test with these practically very important types of entities.  ...  A data structure is introduced, that allows the efficient processing of large amounts of statistical tests involving geometric entities.  ...  Since classical multi-dimensional data structures do not support statistical geometric tests as query, the running time for sequentially comparing all N line segments with the given one is shown in the  ... 
doi:10.1007/978-3-540-28649-3_46 fatcat:z4nvugzj2bgc7eklvgdifb5kam

Helly-Type Theorems in Property Testing [chapter]

Sourav Chakraborty, Rameshwar Pratap, Sasanka Roy, Shubhangi Saraf
2014 Lecture Notes in Computer Science  
Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability.  ...  If S is a set of n points in R d , we say that S is (k, G)-clusterable if it can be partitioned into k clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object  ...  For (1, A) -cluster testing in a symmetric convex body A, we showed that testing can be done with constant number of queries and hence proved that the property is testable. Alon et al.  ... 
doi:10.1007/978-3-642-54423-1_27 fatcat:zjpkcacguveh7hvsa55jlicbcy

An Automated Approach for the Discovery of Interoperability [article]

Duygu Sap, Daniel P. Szabo
2020 arXiv   pre-print
Our analysis is based on utilizing queries in deriving the shape properties and constructing the proxy models of the given CAD models [1].  ...  the interoperability testing.  ...  , namely, geometric, topological and integral properties.  ... 
arXiv:2001.10585v1 fatcat:bxq7ni6itfd4bav7gnghocafbu

Consistent Roof Geometry Encoding for 3D Building Model Retrieval Using Airborne LiDAR Point Clouds

2017 ISPRS International Journal of Geo-Information  
However, the use of low-frequency SHs decreases the ability to distinguish objects with similar geometric shapes thereby leading to ambiguity in shape description.  ...  The depth images are further encoded by geometry features with spatial histograms, which introduce the properties of compact description, rotation invariance, noise insensitivity, and consistent encoding  ...  Three building point clouds were tested as the input queries.  ... 
doi:10.3390/ijgi6090269 fatcat:p5bl7tecdzhyjpno3wt7eapdzu

Helly-Type Theorems in Property Testing [article]

Sourav Chakraborty, Rameshwar Pratap, Sasanka Roy, Shubhangi Saraf
2013 arXiv   pre-print
Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability.  ...  If S is a set of n points in R^d, we say that S is (k,G)-clusterable if it can be partitioned into k clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object  ...  Property Testing In property testing, the goal is to query a very small fraction of the input and decide whether the input satisfies a certain predetermined property or is "far" from satisfying it.  ... 
arXiv:1307.8268v2 fatcat:tgjkwnrz45eppo4ebk73xuqd34
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