TY - GEN

T1 - On piercing sets of axis-parallel rectangles and rings

AU - Segal, Michael

N1 - Publisher Copyright:
© 1997, Springer Verlag, All Rights Reserved.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We consider the p-piercing problem for axis-parallel rectangles. We are given a collection of axis-paxallel rectangles in the plane, and wish to determine whether there exists a set of p points whose union intersects all the given rectangles. We present efficient algorithms for finding a piercing set (i.e., a set of p points as above) for values of p = 1,2, 3, 4,5. The result for 4 and 5-piercing improves an existing result of O(n log3 n) and O(n log4n) to O(n log n) time, and is applied to find a better rectilinear 5-center agorithm. We improve the existing algorithm for general (but fixed) p, and we also extend our algorithms to higher dimensional space. We also consider the problem of piercing a set of rectaJagular rings.

AB - We consider the p-piercing problem for axis-parallel rectangles. We are given a collection of axis-paxallel rectangles in the plane, and wish to determine whether there exists a set of p points whose union intersects all the given rectangles. We present efficient algorithms for finding a piercing set (i.e., a set of p points as above) for values of p = 1,2, 3, 4,5. The result for 4 and 5-piercing improves an existing result of O(n log3 n) and O(n log4n) to O(n log n) time, and is applied to find a better rectilinear 5-center agorithm. We improve the existing algorithm for general (but fixed) p, and we also extend our algorithms to higher dimensional space. We also consider the problem of piercing a set of rectaJagular rings.

UR - http://www.scopus.com/inward/record.url?scp=84949195923&partnerID=8YFLogxK

U2 - 10.1007/3-540-63397-9_33

DO - 10.1007/3-540-63397-9_33

M3 - Conference contribution

AN - SCOPUS:84949195923

SN - 3540633979

SN - 9783540633976

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

SP - 430

EP - 442

BT - Algorithms - ESA 1997 - 5th Annual European Symposium, Proceedings

A2 - Burkard, Rainer

A2 - Woeginger, Gerhard

PB - Springer Verlag

T2 - 5th Annual European Symposium on Algorithms, ESA 1997

Y2 - 15 September 1997 through 17 September 1997

ER -