Fast algorithms for collision and proximity problems involving moving geometric objects

Prosenjit Gupta, Ravi Janardan, Michiel Smid

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


Consider a set of geometric objects, such as points or axes-parallel hyper-rectangles in IRd, that move with constant but possibly different velocities along linear trajectories. Efficient algorithms are presented for several problems defined on such objects, such as determining whether any two objects ever collide and computing the minimum inter-point separation or minimum diameter that ever occurs. In particular, two open problems from the literature are solved: Deciding in o(n2) time if there is a collision in a set of n moving points in IR2, where the points move at constant but possibly different velocities, and the analogous problem for detecting a red-blue collision between sets of red and blue moving points. The strategy used involves reducing the given problem on moving objects to a different problem on a set of static objects, and then solving the latter problem using techniques based on sweeping, orthogonal range searching, simplex composition, and parametric search.

Original languageEnglish (US)
Title of host publicationAlgorithms - ESA'94 - 2nd Annual European Symposium, Proceedings
EditorsJan van Leeuwen
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540584346
StatePublished - 1994
Event2nd Annual European Symposium on Algorithms, ESA 1994 - Utrecht, Netherlands
Duration: Sep 26 1994Sep 28 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume855 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other2nd Annual European Symposium on Algorithms, ESA 1994

Bibliographical note

Funding Information:
The research of these authors was supported in part by NSF grant CCRa-92-00270. This author was supported by the ESPRIT Basic Research Actions Program, under contract No. 7141 (project ALCOM II).

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.


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