TY - GEN

T1 - An optimal algorithm for finding the separation of simple polygons

AU - Amato, Nancy M.

PY - 1993

Y1 - 1993

N2 - Given simple polygons P and Q, their separation, denoted by σ(P,Q), is defined to be the minimum distance between their boundaries. We present an optimal Θ(N) algorithm for determining the separation of two simple polygons P and Q, where |P|+|Q|=|N|. The best previous algorithm for this problem is due to Kirkpatrick and has complexity O(N log N). In addition, a parallel version of our algorithm can be implemented in O(log N) time using O(N) processors on a CREW PRAM. Our results are obtained by providing a unified treatment of the separation and the closest visible vertex problems for simple polygons.

AB - Given simple polygons P and Q, their separation, denoted by σ(P,Q), is defined to be the minimum distance between their boundaries. We present an optimal Θ(N) algorithm for determining the separation of two simple polygons P and Q, where |P|+|Q|=|N|. The best previous algorithm for this problem is due to Kirkpatrick and has complexity O(N log N). In addition, a parallel version of our algorithm can be implemented in O(log N) time using O(N) processors on a CREW PRAM. Our results are obtained by providing a unified treatment of the separation and the closest visible vertex problems for simple polygons.

UR - http://www.scopus.com/inward/record.url?scp=21144469096&partnerID=8YFLogxK

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U2 - 10.1007/3-540-57155-8_235

DO - 10.1007/3-540-57155-8_235

M3 - Conference contribution

AN - SCOPUS:21144469096

SN - 9783540571551

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 48

EP - 59

BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Santoro, Nicola

A2 - Whitesides, Sue

PB - Springer-Verlag Berlin Heidelberg

T2 - 3rd Workshop on Algorithms and Data Structures, WADS 1993

Y2 - 11 August 1993 through 13 August 1993

ER -