Improvements on geometric pattern matching problems

L. Paul Chew; Klara Kedem

doi:10.1007/3-540-55706-7_28

Improvements on geometric pattern matching problems

L. Paul Chew, Klara Kedem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

37 Scopus citations

Abstract

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).

Original language	English
Title of host publication	Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings
Editors	Otto Nurmi, Esko Ukkonen
Publisher	Springer Verlag
Pages	318-325
Number of pages	8
ISBN (Print)	9783540557067
DOIs	https://doi.org/10.1007/3-540-55706-7_28
State	Published - 1 Jan 1992
Externally published	Yes
Event	3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992 - Helsinki, Finland Duration: 8 Jul 1992 → 10 Jul 1992

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	621 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992
Country/Territory	Finland
City	Helsinki
Period	8/07/92 → 10/07/92

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-55706-7_28

Cite this

Chew, L. P., & Kedem, K. (1992). Improvements on geometric pattern matching problems. In O. Nurmi, & E. Ukkonen (Eds.), Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings (pp. 318-325). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 621 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55706-7_28

Chew, L. Paul ; Kedem, Klara. / Improvements on geometric pattern matching problems. Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings. editor / Otto Nurmi ; Esko Ukkonen. Springer Verlag, 1992. pp. 318-325 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Improvements on geometric pattern matching problems",

abstract = "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).",

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Chew, LP & Kedem, K 1992, Improvements on geometric pattern matching problems. in O Nurmi & E Ukkonen (eds), Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 621 LNCS, Springer Verlag, pp. 318-325, 3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992, Helsinki, Finland, 8/07/92. https://doi.org/10.1007/3-540-55706-7_28

Improvements on geometric pattern matching problems. / Chew, L. Paul; Kedem, Klara.
Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings. ed. / Otto Nurmi; Esko Ukkonen. Springer Verlag, 1992. p. 318-325 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 621 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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).

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Chew LP, Kedem K. Improvements on geometric pattern matching problems. In Nurmi O, Ukkonen E, editors, Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings. Springer Verlag. 1992. p. 318-325. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-55706-7_28

Improvements on geometric pattern matching problems

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