The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Cutting hyperplane arrangements
Discrete & Computational Geometry
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Intersection queries in curved objects
Journal of Algorithms
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Connected Component and Simple Polygon Intersection Searching (Extended Abstract)
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Optimal and near-optimal algorithms for generalized intersection reporting on pointer machines
Information Processing Letters
A new framework for addressing temporal range queries and some preliminary results
Theoretical Computer Science
Chromatic distribution of k-nearest neighbors of a line segment in a planar colored point set
Information Processing Letters
Optimal and near-optimal algorithms for generalized intersection reporting on pointer machines
Information Processing Letters
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Generalized intersection searching problems are a class of geometric query-retrieval problems where the questions of interest concern the intersection of a query object with aggregates of geometric objects (rather than with individual objects.) This class contains, as a special case, the well-studied class of standard intersection searching problems and is rich in applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the aggregates satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving non-iso-oriented objects. These problems include: generalized halfspace range searching, segment intersection searching, triangle stabbing, and triangle range searching. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.