4 Search Results for "Rubinstein, Ittai"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.18
q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations

Authors: Kiril Bangachev and S. Matthew Weinberg

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3). For domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following: 1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. 2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest. We also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019].
Cite as

Kiril Bangachev and S. Matthew Weinberg. q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.3
Near-Optimal Trace Reconstruction for Mildly Separated Strings

Authors: Anders Aamand, Allen Liu, and Shyam Narayanan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In the trace reconstruction problem our goal is to learn an unknown string x ∈ {0,1}ⁿ given independent traces of x. A trace is obtained by independently deleting each bit of x with some probability δ and concatenating the remaining bits. It is a major open question whether the trace reconstruction problem can be solved with a polynomial number of traces when the deletion probability δ is constant. The best known upper bound and lower bounds are respectively exp(Õ(n^{1/5})) [Zachary Chase, 2021a] and ̃ Ω(n^{3/2}) [Zachary Chase, 2021b]. Our main result is that if the string x is mildly separated, meaning that the number of zeros between any two ones in x is at least polylog n, and if δ is a sufficiently small constant, then the trace reconstruction problem can be solved with O(n log n) traces and in polynomial time.
Cite as

Anders Aamand, Allen Liu, and Shyam Narayanan. Near-Optimal Trace Reconstruction for Mildly Separated Strings. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aamand_et_al:LIPIcs.ICALP.2025.3,
  author =	{Aamand, Anders and Liu, Allen and Narayanan, Shyam},
  title =	{{Near-Optimal Trace Reconstruction for Mildly Separated Strings}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.3},
  URN =		{urn:nbn:de:0030-drops-233801},
  doi =		{10.4230/LIPIcs.ICALP.2025.3},
  annote =	{Keywords: Trace Reconstruction, deletion channel, sample complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.102
Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem

Authors: Ittai Rubinstein

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

Abstract
In the trace reconstruction problem, one is given many outputs (called traces) of a noise channel applied to the same input message x, and is asked to recover the input message. Common noise channels studied in the context of trace reconstruction include the deletion channel which deletes each bit w.p. δ, the insertion channel which inserts a G_j i.i.d. uniformly distributed bits before each bit of the input message (where G_j is i.i.d. geometrically distributed with parameter σ) and the symmetry channel which flips each bit of the input message i.i.d. w.p. γ. De et al. and Nazarov and Peres [De et al., 2017; Nazarov and Peres, 2017] showed that any string x can be reconstructed from exp(O(n^{1/3})) traces. Holden et al. [Holden et al., 2018] adapted the techniques used to prove this upper bound, to construct an algorithm for average-case trace reconstruction from the insertion-deletion channel with a sample complexity of exp(O(log^{1/3} n)). However, it is not clear how to apply their techniques more generally and in particular for the recent worst-case upper bound of exp(Õ(n^{1/5})) shown by Chase [Chase, 2021] for the deletion channel. We prove a general reduction from the average-case to smaller instances of a problem similar to worst-case and extend Chase’s upper-bound to this problem and to symmetry and insertion channels as well. Using this reduction and generalization of Chase’s bound, we introduce an algorithm for the average-case trace reconstruction from the symmetry-insertion-deletion channel with a sample complexity of exp(Õ(log^{1/5} n)).
Cite as

Ittai Rubinstein. Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rubinstein:LIPIcs.ICALP.2023.102,
  author =	{Rubinstein, Ittai},
  title =	{{Average-Case to (Shifted) Worst-Case Reduction for the Trace Reconstruction Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{102:1--102:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.102},
  URN =		{urn:nbn:de:0030-drops-181542},
  doi =		{10.4230/LIPIcs.ICALP.2023.102},
  annote =	{Keywords: Trace Reconstruction, Synchronization Channels, Computational Learning Theory, Computational Biology}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.105
Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel

Authors: Ittai Rubinstein

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter p (BDC_p) - a channel where every bit of the codeword is deleted i.i.d with probability p, and the Poisson Repeat Channel with parameter λ (PRC_λ) - a channel where every bit of the codeword is repeated Poisson(λ) times. Previous constructions based on synchronisation strings yielded codes with rates far lower than the capacities of these channels [Con and Shpilka, 2019; Guruswami and Li, 2018], and the only efficient construction to achieve capacity on the BDC at the time of writing this paper is based on the far more advanced methods of polar codes [Tal et al., 2021]. In this work, we present a new method for concatenating synchronisation codes and use it to construct simple and efficient encoding and decoding algorithms for both channels with nearly optimal rates.
Cite as

Ittai Rubinstein. Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 105:1-105:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein:LIPIcs.ICALP.2022.105,
  author =	{Rubinstein, Ittai},
  title =	{{Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{105:1--105:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.105},
  URN =		{urn:nbn:de:0030-drops-164466},
  doi =		{10.4230/LIPIcs.ICALP.2022.105},
  annote =	{Keywords: Error Correcting Codes, Algorithmic Coding Theory, Binary Deletion Channel}
}
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