A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A complete roundness classification procedure
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Handbook of discrete and computational geometry
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Map labeling and its generalizations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Testing the Quality of Manufactured Balls
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Testing the Quality of Manufactured Disks and Cylinders
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Property Testing in Computational Geometry
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Property testing
Property testing
Property testing
Property testing
Online geometric reconstruction
Journal of the ACM (JACM)
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This paper investigates geometric problems in the context of property testing algorithms. Property testing is an emerging area in computer science in which one is aiming at verifying whether a given object has a predetermined property or is "far" from any object having the property. 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 is "far" or it is "close"; very little research has been done for geometric notion of distance measures, that is, distance measures that are based on the geometry underlying input objects. The main objective of this work is to develop sound models to study geometric problems in the context of property testing. Comparing to the previous work in property testing, there are two novel aspects developed in this paper: geometric measures of being close to an object having the predetermined property, and the use of geometric data structures as basic primitives to design the testers.We believe that the second aspect is of special importance in the context of property testing and that the use of specialized data structures as basic primitives in the testers can be applied to other important problems in this area. We shall discuss a number of models that in our opinion fit best geometric problems and apply them to study geometric properties for three very fundamental and representative problems in the area: testing convex position, testing map labeling, and testing clusterability.