Abstract
Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |
| Publisher | ACM |
| Pages | 301-310 |
| Number of pages | 10 |
| State | Published - 1996 |
| Externally published | Yes |
| Event | Proceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA Duration: May 24 1996 → May 26 1996 |
Other
| Other | Proceedings of the 1996 12th Annual Symposium on Computational Geometry |
|---|---|
| City | Philadelphia, PA, USA |
| Period | 5/24/96 → 5/26/96 |
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ASJC Scopus subject areas
- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology
Cite this
Improvements on bottleneck matching and related problems using geometry. / Efrat, Alon; Itai, Alon.
Proceedings of the Annual Symposium on Computational Geometry. ACM, 1996. p. 301-310.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Improvements on bottleneck matching and related problems using geometry
AU - Efrat, Alon
AU - Itai, Alon
PY - 1996
Y1 - 1996
N2 - Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.
AB - Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.
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UR - http://www.scopus.com/inward/citedby.url?scp=0029715023&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0029715023
SP - 301
EP - 310
BT - Proceedings of the Annual Symposium on Computational Geometry
PB - ACM
ER -