Reporting All Segment Intersections Using an Arbitrary Sized Work Space

Matsuo KONAGAYA  Tetsuo ASANO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.6   pp.1066-1071
Publication Date: 2013/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1066
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
computational geometry,  adjustable work space algorithm,  segment intersection detection and reporting,  isothetic segment,  read-only input model,  

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This paper presents an efficient algorithm for reporting all intersections among n given segments in the plane using work space of arbitrarily given size. More exactly, given a parameter s which is between Ω(1) and O(n) specifying the size of work space, the algorithm reports all the segment intersections in roughly O(n2/+ K) time using O(s) words of O(log n) bits, where K is the total number of intersecting pairs. The time complexity can be improved to O((n2/s) log s + K) when input segments have only some number of different slopes.