On-line zone construction in arrangements of lines in the plane

Yuval Aharoni, Dan Halperin, Iddo Hanniel, Sariel Har-Peled, Chaim Linhart

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Given a nite set L of lines in the plane we wish to compute the zone of an additional curve in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by, where is not given in advance but rather provided online portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a iscussion of the advantages and shortcomings of each of the proposed algorithms.

Original languageEnglish
Title of host publicationAlgorithm Engineering - 3rd International Workshop, WAE 1999, Proceedings
EditorsJeffrey S. Vitter, Christos D. Zaroliagis
PublisherSpringer Verlag
Number of pages1
ISBN (Print)3540664270, 9783540664277
StatePublished - 1999
Event3rd International Workshop on Algorithm Engineering, WAE 1999 - London, United Kingdom
Duration: 19 Jul 199921 Jul 1999

Publication series

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


Conference3rd International Workshop on Algorithm Engineering, WAE 1999
Country/TerritoryUnited Kingdom


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