Space-efficient ray-shooting and intersection searching: Algorithms, dynamization, and applications

Siu Wing Cheng, Ravi Janardan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

Space-efficient algorithms are presented for a number of intersection searching problems in the plane, including, ray-shooting, segment intersection searching, triangle stabbing, and triangle range searching. The algorithms for ray-shooting and segment intersection searching are improvements upon the results given previously in [Aga89]. All the algorithms can be dynamized efficiently by taking advantage of their decomposability. Several applications of the above results are presented.

Original languageEnglish (US)
Title of host publicationProceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991
PublisherAssociation for Computing Machinery
Pages7-16
Number of pages10
ISBN (Print)0897913760
StatePublished - Mar 1 1991
Event2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 - San Francisco, United States
Duration: Jan 28 1991Jan 30 1991

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991
CountryUnited States
CitySan Francisco
Period1/28/911/30/91

Bibliographical note

Funding Information:
We improve upon the result in [Aga89] by construct-ing a structure for ray-shooting in an arrangement of possibly intersecting segments that achieves O(n log3 n) space and O(@ log n) query time. For non-intersecting segments, the space is improvable to O(n log2 n). The preprocessing time is the same as in [Aga89], namely, O(n@logW n), where w is a constant less than 4.3. As in [Aga89], our result also makes extensive use of spanning trees of low stabbing number. We also ex-tend the ray-shooting s~ructure to solve the general seg-ment intersection ~earching problem. Our algorithm uses O(n log3 n) space and reports in O(min{filog n + k log n, @ log2 n + k}) time the k intersections between a query segment and n possibly intersecting segments. The space can be improved to O(n log2 n) for non-intersecting segments. However, the query time will then increase slightly to O(fi log n + k log n). In [Aga89], an O(@ log2 n + k log n) query time is claimed for the case of a query ray and n non-intersecting segments, but the general problem is left open. Using a different method, Overmars et al. [0 SS89] construct O(n log n)-space and O(n~ log n + /c)-query time data structures for both non-intersecting and intersecting segments. “Department of Computer Science,University of Mhmesota,Minneapolis, MN 55455.Authors’ e-mail addresses:scheng(hurm-csc.a.umn.edu, janardantkmn-cs. cs.umn.edu. +T& resem&was supportedinpartbyagrant-in-aidofresearchfromtheGraduateSchOOl of the University of Minnesota. The secondauthor was also supported in part by NSF grant CCR-8808574.

Publisher Copyright:
© 1991 Association for Computing Machinery. All rights reserved.

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