87 Search Results for "Chakrabarti, Amit"


Volume

LIPIcs, Volume 245

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

APPROX/RANDOM 2022, September 19-21, 2022, University of Illinois, Urbana-Champaign, USA (Virtual Conference)

Editors: Amit Chakrabarti and Chaitanya Swamy

Document
New Lower Bounds in Merlin-Arthur Communication and Graph Streaming Verification

Authors: Prantar Ghosh and Vihan Shah

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We present novel lower bounds in the Merlin-Arthur (MA) communication model and the related annotated streaming or stream verification model. The MA communication model extends the classical communication model by introducing an all-powerful but untrusted player, Merlin, who knows the inputs of the usual players, Alice and Bob, and attempts to convince them about the output. We focus on the online MA (OMA) model where Alice and Merlin each send a single message to Bob, who needs to catch Merlin if he is dishonest and announce the correct output otherwise. Most known functions have OMA protocols with total communication significantly smaller than what would be needed without Merlin. In this work, we introduce the notion of non-trivial-OMA complexity of a function. This is the minimum total communication required when we restrict ourselves to only non-trivial protocols where Alice sends Bob fewer bits than what she would have sent without Merlin. We exhibit the first explicit functions that have this complexity superlinear - even exponential - in their classical one-way complexity: this means the trivial protocol, where Merlin communicates nothing and Alice and Bob compute the function on their own, is exponentially better than any non-trivial protocol in terms of total communication. These OMA lower bounds also translate to the annotated streaming model, the MA analogue of single-pass data streaming. We show large separations between the classical streaming complexity and the non-trivial annotated streaming complexity (for the analogous notion in this setting) of fundamental problems such as counting distinct items, as well as of graph problems such as connectivity and k-connectivity in a certain edge update model called the support graph turnstile model that we introduce here.

Cite as

Prantar Ghosh and Vihan Shah. New Lower Bounds in Merlin-Arthur Communication and Graph Streaming Verification. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 53:1-53:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{ghosh_et_al:LIPIcs.ITCS.2024.53,
  author =	{Ghosh, Prantar and Shah, Vihan},
  title =	{{New Lower Bounds in Merlin-Arthur Communication and Graph Streaming Verification}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{53:1--53:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.53},
  URN =		{urn:nbn:de:0030-drops-195815},
  doi =		{10.4230/LIPIcs.ITCS.2024.53},
  annote =	{Keywords: Graph Algorithms, Streaming, Communication Complexity, Stream Verification, Merlin-Arthur Communication, Lower Bounds}
}
Document
Complete Volume
LIPIcs, Volume 245, APPROX/RANDOM 2022, Complete Volume

Authors: Amit Chakrabarti and Chaitanya Swamy

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
LIPIcs, Volume 245, APPROX/RANDOM 2022, Complete Volume

Cite as

Amit Chakrabarti and Chaitanya Swamy. LIPIcs, Volume 245, APPROX/RANDOM 2022, Complete Volume. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 1-1064, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@Proceedings{chakrabarti_et_al:LIPIcs.APPROX/RANDOM.2022,
  title =	{{LIPIcs, Volume 245, APPROX/RANDOM 2022, Complete Volume}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{1--1064},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022},
  URN =		{urn:nbn:de:0030-drops-171211},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022},
  annote =	{Keywords: LIPIcs, Volume 245, APPROX/RANDOM 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Amit Chakrabarti and Chaitanya Swamy

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Amit Chakrabarti and Chaitanya Swamy. Front Matter, Table of Contents, Preface, Conference Organization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 0:i-0:xx, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{chakrabarti_et_al:LIPIcs.APPROX/RANDOM.2022.0,
  author =	{Chakrabarti, Amit and Swamy, Chaitanya},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.0},
  URN =		{urn:nbn:de:0030-drops-171229},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
RANDOM
A Unified Approach to Discrepancy Minimization

Authors: Nikhil Bansal, Aditi Laddha, and Santosh Vempala

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of the method by deriving a discrepancy bound for smoothed instances, which interpolates between known bounds for worst-case and random instances.

Cite as

Nikhil Bansal, Aditi Laddha, and Santosh Vempala. A Unified Approach to Discrepancy Minimization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 1:1-1:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{bansal_et_al:LIPIcs.APPROX/RANDOM.2022.1,
  author =	{Bansal, Nikhil and Laddha, Aditi and Vempala, Santosh},
  title =	{{A Unified Approach to Discrepancy Minimization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.1},
  URN =		{urn:nbn:de:0030-drops-171238},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.1},
  annote =	{Keywords: Discrepancy theory, smoothed analysis}
}
Document
RANDOM
Fourier Growth of Regular Branching Programs

Authors: Chin Ho Lee, Edward Pyne, and Salil Vadhan

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We analyze the Fourier growth, i.e. the L₁ Fourier weight at level k (denoted L_{1,k}), of read-once regular branching programs. We prove that every read-once regular branching program B of width w ∈ [1,∞] with s accepting states on n-bit inputs must have its L_{1,k} bounded by min{Pr[B(U_n) = 1](w-1)^k, s ⋅ O((n log n)/k)^{(k-1)/2}}. For any constant k, our result is tight up to constant factors for the AND function on w-1 bits, and is tight up to polylogarithmic factors for unbounded width programs. In particular, for k = 1 we have L_{1,1}(B) ≤ s, with no dependence on the width w of the program. Our result gives new bounds on the coin problem and new pseudorandom generators (PRGs). Furthermore, we obtain an explicit generator for unordered permutation branching programs of unbounded width with a constant factor stretch, where no PRG was previously known. Applying a composition theorem of Błasiok, Ivanov, Jin, Lee, Servedio and Viola (RANDOM 2021), we extend our results to "generalized group products," a generalization of modular sums and product tests.

Cite as

Chin Ho Lee, Edward Pyne, and Salil Vadhan. Fourier Growth of Regular Branching Programs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{lee_et_al:LIPIcs.APPROX/RANDOM.2022.2,
  author =	{Lee, Chin Ho and Pyne, Edward and Vadhan, Salil},
  title =	{{Fourier Growth of Regular Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.2},
  URN =		{urn:nbn:de:0030-drops-171247},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.2},
  annote =	{Keywords: pseudorandomness, fourier analysis}
}
Document
RANDOM
Double Balanced Sets in High Dimensional Expanders

Authors: Tali Kaufman and David Mass

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
Recent works have shown that expansion of pseudorandom sets is of great importance. However, all current works on pseudorandom sets are limited only to product (or approximate product) spaces, where Fourier Analysis methods could be applied. In this work we ask the natural question whether pseudorandom sets are relevant in domains where Fourier Analysis methods cannot be applied, e.g., one-sided local spectral expanders. We take the first step in the path of answering this question. We put forward a new definition for pseudorandom sets, which we call "double balanced sets". We demonstrate the strength of our new definition by showing that small double balanced sets in one-sided local spectral expanders have very strong expansion properties, such as unique-neighbor-like expansion. We further show that cohomologies in cosystolic expanders are double balanced, and use the newly derived strong expansion properties of double balanced sets in order to obtain an exponential improvement over the current state of the art lower bound on their minimal distance.

Cite as

Tali Kaufman and David Mass. Double Balanced Sets in High Dimensional Expanders. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 3:1-3:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{kaufman_et_al:LIPIcs.APPROX/RANDOM.2022.3,
  author =	{Kaufman, Tali and Mass, David},
  title =	{{Double Balanced Sets in High Dimensional Expanders}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.3},
  URN =		{urn:nbn:de:0030-drops-171257},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.3},
  annote =	{Keywords: High dimensional expanders, Double balanced sets, Pseudorandom functions}
}
Document
RANDOM
Fast and Perfect Sampling of Subgraphs and Polymer Systems

Authors: Antonio Blanca, Sarah Cannon, and Will Perkins

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a percolation subcriticality condition. We show that this condition is optimal in the sense that the task of (approximately) sampling weighted rooted graphlets becomes impossible in finite expected time for infinite graphs and intractable for finite graphs when the condition does not hold. We apply our sampling algorithm as a subroutine to give near linear-time perfect sampling algorithms for polymer models and weighted non-rooted graphlets in finite graphs, two widely studied yet very different problems. This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications.

Cite as

Antonio Blanca, Sarah Cannon, and Will Perkins. Fast and Perfect Sampling of Subgraphs and Polymer Systems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 4:1-4:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{blanca_et_al:LIPIcs.APPROX/RANDOM.2022.4,
  author =	{Blanca, Antonio and Cannon, Sarah and Perkins, Will},
  title =	{{Fast and Perfect Sampling of Subgraphs and Polymer Systems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.4},
  URN =		{urn:nbn:de:0030-drops-171261},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.4},
  annote =	{Keywords: Random Sampling, perfect sampling, graphlets, polymer models, spin systems, percolation}
}
Document
RANDOM
High Dimensional Expansion Implies Amplified Local Testability

Authors: Tali Kaufman and Izhar Oppenheim

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
In this work, we define a notion of local testability of codes that is strictly stronger than the basic one (studied e.g., by recent works on high rate LTCs), and we term it amplified local testability. Amplified local testability is a notion close to the result of optimal testing for Reed-Muller codes achieved by Bhattacharyya et al. We present a scheme to get amplified locally testable codes from high dimensional expanders. We show that single orbit Affine invariant codes, and in particular Reed-Muller codes, can be described via our scheme, and hence are amplified locally testable. This gives the strongest currently known testability result of single orbit affine invariant codes, strengthening the celebrated result of Kaufman and Sudan.

Cite as

Tali Kaufman and Izhar Oppenheim. High Dimensional Expansion Implies Amplified Local Testability. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 5:1-5:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{kaufman_et_al:LIPIcs.APPROX/RANDOM.2022.5,
  author =	{Kaufman, Tali and Oppenheim, Izhar},
  title =	{{High Dimensional Expansion Implies Amplified Local Testability}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{5:1--5:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.5},
  URN =		{urn:nbn:de:0030-drops-171276},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.5},
  annote =	{Keywords: Locally testable codes, High dimensional expanders, Amplified testing}
}
Document
RANDOM
Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs

Authors: Uma Girish, Kunal Mittal, Ran Raz, and Wei Zhan

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We prove that for every 3-player (3-prover) game G with value less than one, whose query distribution has the support S = {(1,0,0), (0,1,0), (0,0,1)} of Hamming weight one vectors, the value of the n-fold parallel repetition G^{⊗n} decays polynomially fast to zero; that is, there is a constant c = c(G) > 0 such that the value of the game G^{⊗n} is at most n^{-c}. Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC 2022), our result is the missing piece that implies a similar bound for a much more general class of multiplayer games: For every 3-player game G over binary questions and arbitrary answer lengths, with value less than 1, there is a constant c = c(G) > 0 such that the value of the game G^{⊗n} is at most n^{-c}. Our proof technique is new and requires many new ideas. For example, we make use of the Level-k inequalities from Boolean Fourier Analysis, which, to the best of our knowledge, have not been explored in this context prior to our work.

Cite as

Uma Girish, Kunal Mittal, Ran Raz, and Wei Zhan. Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 6:1-6:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{girish_et_al:LIPIcs.APPROX/RANDOM.2022.6,
  author =	{Girish, Uma and Mittal, Kunal and Raz, Ran and Zhan, Wei},
  title =	{{Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.6},
  URN =		{urn:nbn:de:0030-drops-171286},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.6},
  annote =	{Keywords: Parallel repetition, Multi-prover games, Fourier analysis}
}
Document
RANDOM
Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks

Authors: Hermish Mehta and Daniel Reichman

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all k-vertex subgraphs of an n-vertex graph. When k is not too large, we give nearly tight bounds for this local treewidth parameter; we also derive nearly tight bounds for the local treewidth of noisy trees, trees where every non-edge is added independently with small probability. We apply our upper bounds on the local treewidth to obtain fixed parameter tractable algorithms (on random graphs and noisy trees) for edge-removal problems centered around containing a contagious process evolving over a network. In these problems, our main parameter of study is k, the number of initially "infected" vertices in the network. For the random graph models we consider and a certain range of parameters the running time of our algorithms on n-vertex graphs is 2^o(k) poly(n), improving upon the 2^Ω(k) poly(n) performance of the best-known algorithms designed for worst-case instances of these edge deletion problems.

Cite as

Hermish Mehta and Daniel Reichman. Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{mehta_et_al:LIPIcs.APPROX/RANDOM.2022.7,
  author =	{Mehta, Hermish and Reichman, Daniel},
  title =	{{Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.7},
  URN =		{urn:nbn:de:0030-drops-171299},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.7},
  annote =	{Keywords: Graph Algorithms, Random Graphs, Data Structures and Algorithms, Discrete Mathematics}
}
Document
RANDOM
Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

Authors: Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage. One of the most basic versions of this problem was settled more than 50 years ago by Levenshtein, who proved that binary Varshamov-Tenengolts codes correct one arbitrary edit error, i.e., one deletion or one substitution, with nearly optimal redundancy. However, this approach fails to extend to many simple and natural variations of the binary single-edit error setting. In this work, we make progress on the code design problem above in three such variations: - We construct linear-time encodable and decodable length-n non-binary codes correcting a single edit error with nearly optimal redundancy log n+O(log log n), providing an alternative simpler proof of a result by Cai, Chee, Gabrys, Kiah, and Nguyen (IEEE Trans. Inf. Theory 2021). This is achieved by employing what we call weighted VT sketches, a new notion that may be of independent interest. - We show the existence of a binary code correcting one deletion or one adjacent transposition with nearly optimal redundancy log n+O(log log n). - We construct linear-time encodable and list-decodable binary codes with list-size 2 for one deletion and one substitution with redundancy 4log n+O(log log n). This matches the existential bound up to an O(log log n) additive term.

Cite as

Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu. Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 8:1-8:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{gabrys_et_al:LIPIcs.APPROX/RANDOM.2022.8,
  author =	{Gabrys, Ryan and Guruswami, Venkatesan and Ribeiro, Jo\~{a}o and Wu, Ke},
  title =	{{Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  URN =		{urn:nbn:de:0030-drops-171302},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  annote =	{Keywords: Synchronization errors, Optimal redundancy, Explicit codes}
}
Document
RANDOM
Affine Extractors and AC0-Parity

Authors: Xuangui Huang, Peter Ivanov, and Emanuele Viola

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
We study a simple and general template for constructing affine extractors by composing a linear transformation with resilient functions. Using this we show that good affine extractors can be computed by non-explicit circuits of various types, including AC0-Xor circuits: AC0 circuits with a layer of parity gates at the input. We also show that one-sided extractors can be computed by small DNF-Xor circuits, and separate these circuits from other well-studied classes. As a further motivation for studying DNF-Xor circuits we show that if they can approximate inner product then small AC0-Xor circuits can compute it exactly - a long-standing open problem.

Cite as

Xuangui Huang, Peter Ivanov, and Emanuele Viola. Affine Extractors and AC0-Parity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 9:1-9:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{huang_et_al:LIPIcs.APPROX/RANDOM.2022.9,
  author =	{Huang, Xuangui and Ivanov, Peter and Viola, Emanuele},
  title =	{{Affine Extractors and AC0-Parity}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.9},
  URN =		{urn:nbn:de:0030-drops-171313},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.9},
  annote =	{Keywords: affine extractor, resilient function, constant-depth circuit, parity gate, inner product}
}
Document
RANDOM
Hyperbolic Concentration, Anti-Concentration, and Discrepancy

Authors: Zhao Song and Ruizhe Zhang

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
Chernoff bound is a fundamental tool in theoretical computer science. It has been extensively used in randomized algorithm design and stochastic type analysis. Discrepancy theory, which deals with finding a bi-coloring of a set system such that the coloring of each set is balanced, has a huge number of applications in approximation algorithms design. Chernoff bound [Che52] implies that a random bi-coloring of any set system with n sets and n elements will have discrepancy O(√{n log n}) with high probability, while the famous result by Spencer [Spe85] shows that there exists an O(√n) discrepancy solution. The study of hyperbolic polynomials dates back to the early 20th century when used to solve PDEs by Gårding [Går59]. In recent years, more applications are found in control theory, optimization, real algebraic geometry, and so on. In particular, the breakthrough result by Marcus, Spielman, and Srivastava [MSS15] uses the theory of hyperbolic polynomials to prove the Kadison-Singer conjecture [KS59], which is closely related to discrepancy theory. In this paper, we present a list of new results for hyperbolic polynomials: - We show two nearly optimal hyperbolic Chernoff bounds: one for Rademacher sum of arbitrary vectors and another for random vectors in the hyperbolic cone. - We show a hyperbolic anti-concentration bound. - We generalize the hyperbolic Kadison-Singer theorem [Brä18] for vectors in sub-isotropic position, and prove a hyperbolic Spencer theorem for any constant hyperbolic rank vectors. The classical matrix Chernoff and discrepancy results are based on determinant polynomial which is a special case of hyperbolic polynomials. To the best of our knowledge, this paper is the first work that shows either concentration or anti-concentration results for hyperbolic polynomials. We hope our findings provide more insights into hyperbolic and discrepancy theories.

Cite as

Zhao Song and Ruizhe Zhang. Hyperbolic Concentration, Anti-Concentration, and Discrepancy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 10:1-10:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{song_et_al:LIPIcs.APPROX/RANDOM.2022.10,
  author =	{Song, Zhao and Zhang, Ruizhe},
  title =	{{Hyperbolic Concentration, Anti-Concentration, and Discrepancy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.10},
  URN =		{urn:nbn:de:0030-drops-171324},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.10},
  annote =	{Keywords: Hyperbolic polynomial, Chernoff bound, Concentration, Discrepancy theory, Anti-concentration}
}
Document
RANDOM
Improved Local Testing for Multiplicity Codes

Authors: Dan Karliner and Amnon Ta-Shma

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)


Abstract
Multiplicity codes are a generalization of Reed-Muller codes which include derivatives as well as the values of low degree polynomials, evaluated in every point in 𝔽_p^m. Similarly to Reed-Muller codes, multiplicity codes have a local nature that allows for local correction and local testing. Recently, [Karliner et al., 2022] showed that the plane test, which tests the degree of the codeword on a random plane, is a good local tester for small enough degrees. In this work we simplify and extend the analysis of local testing for multiplicity codes, giving a more general and tight analysis. In particular, we show that multiplicity codes MRM_p(m, d, s) over prime fields with arbitrary d are locally testable by an appropriate k-flat test, which tests the degree of the codeword on a random k-dimensional affine subspace. The relationship between the degree parameter d and the required dimension k is shown to be nearly optimal, and improves on [Karliner et al., 2022] in the case of planes. Our analysis relies on a generalization of the technique of canonincal monomials introduced in [Haramaty et al., 2013]. Generalizing canonical monomials to the multiplicity case requires substantially different proofs which exploit the algebraic structure of multiplicity codes.

Cite as

Dan Karliner and Amnon Ta-Shma. Improved Local Testing for Multiplicity Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 11:1-11:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{karliner_et_al:LIPIcs.APPROX/RANDOM.2022.11,
  author =	{Karliner, Dan and Ta-Shma, Amnon},
  title =	{{Improved Local Testing for Multiplicity Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.11},
  URN =		{urn:nbn:de:0030-drops-171339},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.11},
  annote =	{Keywords: local testing, multiplicity codes, Reed Muller codes}
}
  • Refine by Author
  • 13 Chakrabarti, Amit
  • 6 Ghosh, Prantar
  • 5 Brody, Joshua
  • 4 Guruswami, Venkatesan
  • 4 Woodruff, David P.
  • Show More...

  • Refine by Classification
  • 12 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 8 Theory of computation → Approximation algorithms analysis
  • 8 Theory of computation → Graph algorithms analysis
  • 6 Theory of computation → Streaming models
  • 5 Theory of computation → Design and analysis of algorithms
  • Show More...

  • Refine by Keyword
  • 7 communication complexity
  • 5 Communication complexity
  • 5 data streams
  • 5 graph algorithms
  • 4 Approximation Algorithms
  • Show More...

  • Refine by Type
  • 86 document
  • 1 volume

  • Refine by Publication Year
  • 60 2022
  • 10 2015
  • 7 2014
  • 4 2020
  • 3 2019
  • Show More...

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