Separating Sublinear Time Computations by Approximate Diameter
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Distributed vision with smart pixels
Proceedings of the twenty-fifth annual symposium on Computational geometry
Shortest path queries between geometric objects on surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Property testing
Property testing
Property testing
Property testing
Approximate shortest path queries on weighted polyhedral surfaces
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
SIAM Journal on Discrete Mathematics
A dense hierarchy of sublinear time approximation schemes for bin packing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
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We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons and polyhedra, point location in two-dimensional triangulations and Voronoi diagrams, and ray shooting in convex polyhedra, all of which run in expected time $O(\sqrt{n}\,)$, where $n$ is the size of the input. We also provide sublinear solutions for the approximate evaluation of the volume of a convex polytope and the length of the shortest path between two points on the boundary.