3 Search Results for "Klein, Nathan"

Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2023.1
A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk)

Authors: Anna R. Karlin

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We describe recent joint work with Nathan Klein and Shayan Oveis Gharan showing that for any metric TSP instance, the max entropy algorithm studied by [Anna R. Karlin et al., 2021] returns a solution of expected cost at most 3/2-ε times the cost of the optimal solution to the subtour elimination LP and hence is a 3/2-ε approximation for the metric TSP problem. The research discussed comes from [Anna R. Karlin et al., 2021], [Anna R. Karlin et al., 2022] and [Anna R. Karlin et al., 2022].
Cite as

Anna R. Karlin. A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{karlin:LIPIcs.ICALP.2023.1,
  author =	{Karlin, Anna R.},
  title =	{{A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.1},
  URN =		{urn:nbn:de:0030-drops-180531},
  doi =		{10.4230/LIPIcs.ICALP.2023.1},
  annote =	{Keywords: Traveling Salesperson Problem, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.2
Matroid Partition Property and the Secretary Problem

Authors: Dorna Abdolazimi, Anna R. Karlin, Nathan Klein, and Shayan Oveis Gharan

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
A matroid M on a set E of elements has the α-partition property, for some α > 0, if it is possible to (randomly) construct a partition matroid 𝒫 on (a subset of) elements of M such that every independent set of 𝒫 is independent in M and for any weight function w:E → ℝ_{≥0}, the expected value of the optimum of the matroid secretary problem on 𝒫 is at least an α-fraction of the optimum on M. We show that the complete binary matroid, B_d on 𝔽₂^d does not satisfy the α-partition property for any constant α > 0 (independent of d). Furthermore, we refute a recent conjecture of [Kristóf Bérczi et al., 2021] by showing the same matroid is 2^d/d-colorable but cannot be reduced to an α 2^d/d-colorable partition matroid for any α that is sublinear in d.
Cite as

Dorna Abdolazimi, Anna R. Karlin, Nathan Klein, and Shayan Oveis Gharan. Matroid Partition Property and the Secretary Problem. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abdolazimi_et_al:LIPIcs.ITCS.2023.2,
  author =	{Abdolazimi, Dorna and Karlin, Anna R. and Klein, Nathan and Oveis Gharan, Shayan},
  title =	{{Matroid Partition Property and the Secretary Problem}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{2:1--2:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.2},
  URN =		{urn:nbn:de:0030-drops-175051},
  doi =		{10.4230/LIPIcs.ITCS.2023.2},
  annote =	{Keywords: Online algorithms, Matroids, Matroid secretary problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.27
Locality-Preserving Hashing for Shifts with Connections to Cryptography

Authors: Elette Boyle, Itai Dinur, Niv Gilboa, Yuval Ishai, Nathan Keller, and Ohad Klein

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function h:{0,1}ⁿ → ℤ_n is a (d,δ) locality-preserving hash function for shifts (LPHS) if: (1) h can be computed by (adaptively) querying d bits of its input, and (2) Pr[h(x) ≠ h(x ≪ 1) + 1] ≤ δ, where x is random and ≪ 1 denotes a cyclic shift by one bit to the left. We make the following contributions. - Near-optimal LPHS via Distributed Discrete Log. We establish a general two-way connection between LPHS and algorithms for distributed discrete logarithm in the generic group model. Using such an algorithm of Dinur et al. (Crypto 2018), we get LPHS with near-optimal error of δ = Õ(1/d²). This gives an unusual example for the usefulness of group-based cryptography in a post-quantum world. We extend the positive result to non-cyclic and worst-case variants of LPHS. - Multidimensional LPHS. We obtain positive and negative results for a multidimensional extension of LPHS, making progress towards an optimal 2-dimensional LPHS. - Applications. We demonstrate the usefulness of LPHS by presenting cryptographic and algorithmic applications. In particular, we apply multidimensional LPHS to obtain an efficient "packed" implementation of homomorphic secret sharing and a sublinear-time implementation of location-sensitive encryption whose decryption requires a significantly overlapping view.
Cite as

Elette Boyle, Itai Dinur, Niv Gilboa, Yuval Ishai, Nathan Keller, and Ohad Klein. Locality-Preserving Hashing for Shifts with Connections to Cryptography. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{boyle_et_al:LIPIcs.ITCS.2022.27,
  author =	{Boyle, Elette and Dinur, Itai and Gilboa, Niv and Ishai, Yuval and Keller, Nathan and Klein, Ohad},
  title =	{{Locality-Preserving Hashing for Shifts with Connections to Cryptography}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.27},
  URN =		{urn:nbn:de:0030-drops-156231},
  doi =		{10.4230/LIPIcs.ITCS.2022.27},
  annote =	{Keywords: Sublinear algorithms, metric embeddings, shift finding, discrete logarithm, homomorphic secret sharing}
}
  • Refine by Author
  • 2 Karlin, Anna R.
  • 1 Abdolazimi, Dorna
  • 1 Boyle, Elette
  • 1 Dinur, Itai
  • 1 Gilboa, Niv
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Cryptographic primitives
  • 1 Theory of computation → Nearest neighbor algorithms
  • 1 Theory of computation → Online algorithms
  • 1 Theory of computation → Sketching and sampling

  • Refine by Keyword
  • 1 Matroid secretary problem
  • 1 Matroids
  • 1 Online algorithms
  • 1 Sublinear algorithms
  • 1 Traveling Salesperson Problem
  • Show More...

  • Refine by Type
  • 3 document

  • Refine by Publication Year
  • 2 2023
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact