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Documents authored by Beigi, Salman

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.10
New Algorithmic Directions in Optimal Transport and Applications for Product Spaces

Authors: Salman Beigi, Omid Etesami, Mohammad Mahmoody, and Amir Najafi

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We consider the problem of optimal transport between two high-dimensional distributions μ,ν in ℝⁿ from a new algorithmic perspective, in which we are given a sample x ∼ μ and we have to find a close y ∼ ν while running in poly(n) time, where n is the size/dimension of x,y. In other words, we are interested in making the running time bounded in dimension of the spaces rather than bounded in the total size of the representations of the two distributions. Our main result is a general algorithmic transport result between any product distribution μ and an arbitrary distribution ν of total cost Δ + δ under 𝓁_p^p cost; here Δ is the cost of the so-called Knothe–Rosenblatt transport from μ to ν, while δ is a computational error that goes to zero for larger running time in the transport algorithm. For this result, we need ν to be "sequentially samplable" with a "bounded average sampling cost" which is a novel but natural notion of independent interest. In addition, we prove the following. - We prove an algorithmic version of the celebrated Talagrand’s inequality for transporting the standard Gaussian distribution Φⁿ to an arbitrary ν under the Euclidean-squared cost. When ν is Φⁿ conditioned on a set S of measure ε, we show how to implement the needed sequential sampler for ν in expected time poly(n/ε), using membership oracle access to S. Hence, we obtain an algorithmic transport that maps Φⁿ to Φⁿ|S in time poly(n/ε) and expected Euclidean-squared distance O(log 1/ε), which is optimal for a general set S of measure ε. - As corollary, we find the first computational concentration (Etesami et al. SODA 2020) result for the Gaussian measure under the Euclidean distance with a dimension-independent transportation cost, resolving a question of Etesami et al. More precisely, for any set S of Gaussian measure ε, we map most of Φⁿ samples to S with Euclidean distance O(√{log 1/ε}) in time poly(n/ε).
Cite as

Salman Beigi, Omid Etesami, Mohammad Mahmoody, and Amir Najafi. New Algorithmic Directions in Optimal Transport and Applications for Product Spaces. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beigi_et_al:LIPIcs.ISAAC.2025.10,
  author =	{Beigi, Salman and Etesami, Omid and Mahmoody, Mohammad and Najafi, Amir},
  title =	{{New Algorithmic Directions in Optimal Transport and Applications for Product Spaces}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.10},
  URN =		{urn:nbn:de:0030-drops-249187},
  doi =		{10.4230/LIPIcs.ISAAC.2025.10},
  annote =	{Keywords: Optimal transport, Randomized algorithms, Concentration bounds}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.30
Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources

Authors: Salman Beigi, Andrej Bogdanov, Omid Etesami, and Siyao Guo

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
Let F be a finite alphabet and D be a finite set of distributions over F. A Generalized Santha-Vazirani (GSV) source of type (F, D), introduced by Beigi, Etesami and Gohari (ICALP 2015, SICOMP 2017), is a random sequence (F_1, ..., F_n) in F^n, where F_i is a sample from some distribution d in D whose choice may depend on F_1, ..., F_{i-1}. We show that all GSV source types (F, D) fall into one of three categories: (1) non-extractable; (2) extractable with error n^{-Theta(1)}; (3) extractable with error 2^{-Omega(n)}. We provide essentially randomness-optimal extraction algorithms for extractable sources. Our algorithm for category (2) sources extracts one bit with error epsilon from n = poly(1/epsilon) samples in time linear in n. Our algorithm for category (3) sources extracts m bits with error epsilon from n = O(m + log 1/epsilon) samples in time min{O(m2^m * n),n^{O(|F|)}}. We also give algorithms for classifying a GSV source type (F, D): Membership in category (1) can be decided in NP, while membership in category (3) is polynomial-time decidable.
Cite as

Salman Beigi, Andrej Bogdanov, Omid Etesami, and Siyao Guo. Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{beigi_et_al:LIPIcs.APPROX-RANDOM.2018.30,
  author =	{Beigi, Salman and Bogdanov, Andrej and Etesami, Omid and Guo, Siyao},
  title =	{{Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.30},
  URN =		{urn:nbn:de:0030-drops-94349},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.30},
  annote =	{Keywords: feasibility of randomness extraction, extractor lower bounds, martingales}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.TQC.2015
LIPIcs, Volume 44, TQC'15, Complete Volume

Authors: Salman Beigi and Robert Koenig

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Abstract
LIPIcs, Volume 44, TQC'15, Complete Volume
Cite as

10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Proceedings{beigi_et_al:LIPIcs.TQC.2015,
  title =	{{LIPIcs, Volume 44, TQC'15, Complete Volume}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015},
  URN =		{urn:nbn:de:0030-drops-55649},
  doi =		{10.4230/LIPIcs.TQC.2015},
  annote =	{Keywords: Data Encryption, E.4 Coding and Information Theory, F Theory of Computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TQC.2015.i
Front Matter, Table of Contents, Preface, Committees

Authors: Salman Beigi and Robert König

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Abstract
Front Matter, Table of Contents, Preface, Committees
Cite as

10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. i-xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{beigi_et_al:LIPIcs.TQC.2015.i,
  author =	{Beigi, Salman and K\"{o}nig, Robert},
  title =	{{Front Matter, Table of Contents, Preface, Committees}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{i--xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.i},
  URN =		{urn:nbn:de:0030-drops-55612},
  doi =		{10.4230/LIPIcs.TQC.2015.i},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Committees}
}
Document
DOI: 10.4230/LIPIcs.TQC.2013.192
Symmetries of Codeword Stabilized Quantum Codes

Authors: Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji, Qiang Wang, and Bei Zeng

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Abstract
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant.
Cite as

Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji, Qiang Wang, and Bei Zeng. Symmetries of Codeword Stabilized Quantum Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 192-206, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{beigi_et_al:LIPIcs.TQC.2013.192,
  author =	{Beigi, Salman and Chen, Jianxin and Grassl, Markus and Ji, Zhengfeng and Wang, Qiang and Zeng, Bei},
  title =	{{Symmetries of Codeword Stabilized Quantum Codes}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{192--206},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.192},
  URN =		{urn:nbn:de:0030-drops-43129},
  doi =		{10.4230/LIPIcs.TQC.2013.192},
  annote =	{Keywords: CWS Codes, Union Stabilizer Codes, Permutation Symmetry, Toric Code}
}
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