Low distortion maps between point sets

Claire Kenyon; Yuval Rabani; Alistair Sinclair

doi:10.1145/1007352.1007398

Low distortion maps between point sets

Claire Kenyon^*, Yuval Rabani, Alistair Sinclair

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

37 Scopus citations

Abstract

We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3 + 2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.

Original language	English
Pages (from-to)	272-280
Number of pages	9
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/1007352.1007398
State	Published - 2004
Externally published	Yes
Event	Proceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States Duration: 13 Jun 2004 → 15 Jun 2004

Keywords

Dynamic programming
Low distortion embeddings
Metric spaces
Shape matching

Access to Document

10.1145/1007352.1007398

Cite this

@article{d636a22e30544880a5c6309e4408f48a,

title = "Low distortion maps between point sets",

abstract = "We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3 + 2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.",

keywords = "Dynamic programming, Low distortion embeddings, Metric spaces, Shape matching",

author = "Claire Kenyon and Yuval Rabani and Alistair Sinclair",

year = "2004",

doi = "10.1145/1007352.1007398",

language = "אנגלית",

pages = "272--280",

journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

issn = "0734-9025",

publisher = "Association for Computing Machinery (ACM)",

note = "Proceedings of the 36th Annual ACM Symposium on Theory of Computing ; Conference date: 13-06-2004 Through 15-06-2004",

}

TY - JOUR

T1 - Low distortion maps between point sets

AU - Kenyon, Claire

AU - Rabani, Yuval

AU - Sinclair, Alistair

PY - 2004

Y1 - 2004

N2 - We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3 + 2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.

AB - We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3 + 2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.

KW - Dynamic programming

KW - Low distortion embeddings

KW - Metric spaces

KW - Shape matching

UR - http://www.scopus.com/inward/record.url?scp=4544263872&partnerID=8YFLogxK

U2 - 10.1145/1007352.1007398

DO - 10.1145/1007352.1007398

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.conferencearticle???

AN - SCOPUS:4544263872

SN - 0734-9025

SP - 272

EP - 280

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - Proceedings of the 36th Annual ACM Symposium on Theory of Computing

Y2 - 13 June 2004 through 15 June 2004

ER -

Low distortion maps between point sets

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this