TY - GEN

T1 - Improvements on geometric pattern matching problems

AU - Chew, L. Paul

AU - Kedem, Klara

N1 - Funding Information:
* The first author was supported by AFOSR Grant AFOSR-91-0328, ONR Grant N00014-89-J-1946, NSF Grant IRI-9006137, and DARPA under ONR contract N00014-88-K-0591. The second author was supported by the Eshkol grant 04601-90 from the Israeli Ministry of Science and Technology.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - We consider the following geometric pattern matching problem: find the minimum Hausdorff distance between two point sets under translation with L1 or L∞ as the underlying metric. Huttenlocher, Kedem, and Sharir have shown that this minimum distance can be found by constructing the upper envelope of certain Voronoi surfaces. Further, they show that if the two sets are each of cardinality n then the complexity of the upper envelope of such surfaces is Ω(n3). We examine the question of whether one can get around this cubic lower bound, and show that under the L1 and L∞ metrics, the time to compute the minimum Hausdorff distance between two point sets is On2 log2n).

AB - We consider the following geometric pattern matching problem: find the minimum Hausdorff distance between two point sets under translation with L1 or L∞ as the underlying metric. Huttenlocher, Kedem, and Sharir have shown that this minimum distance can be found by constructing the upper envelope of certain Voronoi surfaces. Further, they show that if the two sets are each of cardinality n then the complexity of the upper envelope of such surfaces is Ω(n3). We examine the question of whether one can get around this cubic lower bound, and show that under the L1 and L∞ metrics, the time to compute the minimum Hausdorff distance between two point sets is On2 log2n).

UR - http://www.scopus.com/inward/record.url?scp=85030530992&partnerID=8YFLogxK

U2 - 10.1007/3-540-55706-7_28

DO - 10.1007/3-540-55706-7_28

M3 - Conference contribution

AN - SCOPUS:85030530992

SN - 9783540557067

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

SP - 318

EP - 325

BT - Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings

A2 - Nurmi, Otto

A2 - Ukkonen, Esko

PB - Springer Verlag

T2 - 3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992

Y2 - 8 July 1992 through 10 July 1992

ER -