The complexity of low-distortion embeddings between point sets

Christos Papadimitriou; Shmuel Safra

The complexity of low-distortion embeddings between point sets

Christos Papadimitriou^*, Shmuel Safra

^*Corresponding author for this work

University of California at Berkeley

Research output: Contribution to conference › Paper › peer-review

31 Scopus citations

Abstract

The first complexity and inapproximability results of the low-distortion embeddings problems between the point sets were discussed. It was proved that it is NP-hard to approximate by a ratio better than 3 the minimum distortion of a bijection between two given finite three-dimensional sets of points. Certain algorithms and hardness results for non-geometric metrics were also derived. The results propose the complexity of minimum distortion in more general settings than those solved as an important open questions.

Original language	English
Pages	112-118
Number of pages	7
State	Published - 2005
Externally published	Yes
Event	Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States Duration: 23 Jan 2005 → 25 Jan 2005

Conference

Conference	Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/Territory	United States
City	Vancouver, BC
Period	23/01/05 → 25/01/05

Cite this

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abstract = "The first complexity and inapproximability results of the low-distortion embeddings problems between the point sets were discussed. It was proved that it is NP-hard to approximate by a ratio better than 3 the minimum distortion of a bijection between two given finite three-dimensional sets of points. Certain algorithms and hardness results for non-geometric metrics were also derived. The results propose the complexity of minimum distortion in more general settings than those solved as an important open questions.",

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AB - The first complexity and inapproximability results of the low-distortion embeddings problems between the point sets were discussed. It was proved that it is NP-hard to approximate by a ratio better than 3 the minimum distortion of a bijection between two given finite three-dimensional sets of points. Certain algorithms and hardness results for non-geometric metrics were also derived. The results propose the complexity of minimum distortion in more general settings than those solved as an important open questions.

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T2 - Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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The complexity of low-distortion embeddings between point sets

Abstract

Conference

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