research-article

Dimension reduction for finite trees in l₁

Authors:

Arnaud de Mesmay,

Mohammad MoharramiAuthors Info & Claims

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

Pages 43 - 50

Published: 17 January 2012 Publication History

Abstract

We show that every n-point tree metric admits a (1 + ε)-embedding into l₁^{C(ε) log n}, for every ε > 0, where C(ε) ≤ O ((1/ε)⁴ log 1/ε)). This matches the natural volume lower bound up to a factor depending only on ε. Previously, it was unknown whether even complete binary trees on n nodes could be embedded in l₁^{O(log n)} with O(1) distortion. For complete d-ary trees, our construction achieves C(ε) ≤ O (½ε²).

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Cited By

Cohen GHaeupler BSchulman LDiakonikolas IKempe DHenzinger M(2018)Explicit binary tree codes with polylogarithmic size alphabetProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188928(535-544)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188928
Lee JMesmay AMoharrami M(2013)Dimension Reduction for Finite Trees in $$\varvec{\ell _1}$$ℓ1Discrete & Computational Geometry10.1007/s00454-013-9536-750:4(977-1032)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1007/s00454-013-9536-7

Index Terms

Dimension reduction for finite trees in l₁
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Trees
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Other conferences

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

January 2012

1764 pages

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Kyoto University: Kyoto University

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 17 January 2012

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SODA '12

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Kyoto University

SODA '12: ACM-SIAM Symposium on Discrete Algorithms

January 17 - 19, 2012

Kyoto, Japan

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Cohen GHaeupler BSchulman LDiakonikolas IKempe DHenzinger M(2018)Explicit binary tree codes with polylogarithmic size alphabetProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188928(535-544)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188928
Lee JMesmay AMoharrami M(2013)Dimension Reduction for Finite Trees in $$\varvec{\ell _1}$$ℓ1Discrete & Computational Geometry10.1007/s00454-013-9536-750:4(977-1032)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1007/s00454-013-9536-7

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