20 Search Results for "Raskhodnikova, Sofya"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.67
Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification

Authors: Esther Galby, Sándor Kisfaludi-Bak, Dániel Marx, and Roohani Sharma

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In the Directed Steiner Network problem, the input is a directed graph G, a set T ⊆ V(G) of k terminals, and a demand graph D on T. The task is to find a subgraph H ⊆ G with the minimum number of edges such that for every (s,t) ∈ E(D), the solution H contains a directed s → t path. The goal of this paper is to investigate how the complexity of the problem depends on the demand pattern in planar graphs. Formally, if 𝒟 is a class of directed graphs, then the 𝒟-Steiner Network (𝒟-DSN) problem is the special case where the demand graph D is restricted to be from 𝒟. We give a complete characterization of the behavior of every 𝒟-DSN problem on planar graphs. We classify every class 𝒟 closed under transitive equivalence and identification of vertices into three cases: assuming ETH, either the problem is 1) solvable in time 2^O(k)⋅n^O(1), i.e., FPT parameterized by the number k of terminals, but not solvable in time 2^o(k)⋅n^O(1), 2) solvable in time f(k)⋅n^O(√k), but cannot be solved in time f(k)⋅n^o(√k), or 3) solvable in time f(k)⋅n^O(k), but cannot be solved in time f(k)⋅n^o(k). Our result is a far-reaching generalization and unification of earlier results on Directed Steiner Tree, Directed Steiner Network, and Strongly Connected Steiner Subgraph on planar graphs. As an important step of our lower bound proof, we discover a rare example of a genuinely planar problem (i.e., described by a planar graph and two sets of vertices) that cannot be solved in time f(k)⋅n^o(k): given two sets of terminals S and T with |S|+|T| = k, find a subgraph with minimum number of edges such that every vertex of T is reachable from every vertex of S.
Cite as

Esther Galby, Sándor Kisfaludi-Bak, Dániel Marx, and Roohani Sharma. Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 67:1-67:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{galby_et_al:LIPIcs.ICALP.2024.67,
  author =	{Galby, Esther and Kisfaludi-Bak, S\'{a}ndor and Marx, D\'{a}niel and Sharma, Roohani},
  title =	{{Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{67:1--67:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.67},
  URN =		{urn:nbn:de:0030-drops-202104},
  doi =		{10.4230/LIPIcs.ICALP.2024.67},
  annote =	{Keywords: Directed Steiner Network, Sub-exponential algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.74
Linear Relaxed Locally Decodable and Correctable Codes Do Not Need Adaptivity and Two-Sided Error

Authors: Guy Goldberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Relaxed locally decodable codes (RLDCs) are error-correcting codes in which individual bits of the message can be recovered by querying only a few bits from a noisy codeword. For uncorrupted codewords, and for every bit, the decoder must decode the bit correctly with high probability. However, for a noisy codeword, a relaxed local decoder is allowed to output a "rejection" symbol, indicating that the decoding failed. We study the power of adaptivity and two-sided error for RLDCs. Our main result is that if the underlying code is linear, adaptivity and two-sided error do not give any power to relaxed local decoding. We construct a reduction from adaptive, two-sided error relaxed local decoders to non-adaptive, one-sided error ones. That is, the reduction produces a relaxed local decoder that never errs or rejects if its input is a valid codeword and makes queries based on its internal randomness (and the requested index to decode), independently of the input. The reduction essentially maintains the query complexity, requiring at most one additional query. For any input, the decoder’s error probability increases at most two-fold. Furthermore, assuming the underlying code is in systematic form, where the original message is embedded as the first bits of its encoding, the reduction also conserves both the code itself and its rate and distance properties We base the reduction on our new notion of additive promise problems. A promise problem is additive if the sum of any two YES-instances is a YES-instance and the sum of any NO-instance and a YES-instance is a NO-instance. This novel framework captures both linear RLDCs and property testing (of linear properties), despite their significant differences. We prove that in general, algorithms for any additive promise problem do not gain power from adaptivity or two-sided error, and obtain the result for RLDCs as a special case. The result also holds for relaxed locally correctable codes (RLCCs), where a codeword bit should be recovered. As an application, we improve the best known lower bound for linear adaptive RLDCs. Specifically, we prove that such codes require block length of n ≥ k^{1+Ω(1/q²)}, where k denotes the message length and q denotes the number of queries.
Cite as

Guy Goldberg. Linear Relaxed Locally Decodable and Correctable Codes Do Not Need Adaptivity and Two-Sided Error. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 74:1-74:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goldberg:LIPIcs.ICALP.2024.74,
  author =	{Goldberg, Guy},
  title =	{{Linear Relaxed Locally Decodable and Correctable Codes Do Not Need Adaptivity and Two-Sided Error}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{74:1--74:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.74},
  URN =		{urn:nbn:de:0030-drops-202174},
  doi =		{10.4230/LIPIcs.ICALP.2024.74},
  annote =	{Keywords: Locally decodable codes, Relaxed locally correctable codes, Relaxed locally decodable codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.112
Testing Spreading Behavior in Networks with Arbitrary Topologies

Authors: Augusto Modanese and Yuichi Yoshida

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given the full topology of a network, how hard is it to test if it is evolving according to a local rule or is far from doing so? Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron (ICALP, 2021), we initiate the study of property testing in dynamic environments with arbitrary topologies. Our focus is on the simplest non-trivial rule that can be tested, which corresponds to the 1-BP rule of bootstrap percolation and models a simple spreading behavior: Every "infected" node stays infected forever, and each "healthy" node becomes infected if and only if it has at least one infected neighbor. Our results are subdivided into two main groups: - If we are testing a single time step of evolution, then the query complexity is O(Δ/ε) or Õ(√n/ε) (whichever is smaller), where Δ and n are the maximum degree of a node and the number of vertices in the underlying graph, respectively. We also give lower bounds for both one- and two-sided error testers that match our upper bounds up to Δ = o(√n) and Δ = O(n^{1/3}), respectively. If ε is constant, then the first of these also holds against adaptive testers. - When testing the environment over T time steps, we have two algorithms that need O(Δ^{T-1}/εT) and Õ(|E|/εT) queries, respectively, where E is the set of edges of the underlying graph. All of our algorithms are one-sided error, and all of them are also non-adaptive, with the single exception of the more complex Õ(√n/ε)-query tester for the case T = 2.
Cite as

Augusto Modanese and Yuichi Yoshida. Testing Spreading Behavior in Networks with Arbitrary Topologies. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 112:1-112:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{modanese_et_al:LIPIcs.ICALP.2024.112,
  author =	{Modanese, Augusto and Yoshida, Yuichi},
  title =	{{Testing Spreading Behavior in Networks with Arbitrary Topologies}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{112:1--112:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.112},
  URN =		{urn:nbn:de:0030-drops-202554},
  doi =		{10.4230/LIPIcs.ICALP.2024.112},
  annote =	{Keywords: Property testing, bootstrap percolation, local phenomena, expander graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.115
On the Cut-Query Complexity of Approximating Max-Cut

Authors: Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [Rubinstein et al., 2018]. Graph algorithms in this cut query model and other query models have recently been studied for various other problems such as min-cut, connectivity, bipartiteness, and triangle detection. Max-cut in the cut query model can also be viewed as a natural special case of submodular function maximization: on query S ⊆ V, the oracle returns the total weight of the cut between S and V\S. Our first main technical result is a lower bound stating that a deterministic algorithm achieving a c-approximation for any c > 1/2 requires Ω(n) queries. This uses an extension of the cut dimension to rule out approximation (prior work of [Graur et al., 2020] introducing the cut dimension only rules out exact solutions). Secondly, we provide a randomized algorithm with Õ(n) queries that finds a c-approximation for any c < 1. We achieve this using a query-efficient sparsifier for undirected weighted graphs (prior work of [Rubinstein et al., 2018] holds only for unweighted graphs). To complement these results, for most constants c ∈ (0,1], we nail down the query complexity of achieving a c-approximation, for both deterministic and randomized algorithms (up to logarithmic factors). Analogously to general submodular function maximization in the same model, we observe a phase transition at c = 1/2: we design a deterministic algorithm for global c-approximate max-cut in O(log n) queries for any c < 1/2, and show that any randomized algorithm requires Ω(n/log n) queries to find a c-approximate max-cut for any c > 1/2. Additionally, we show that any deterministic algorithm requires Ω(n²) queries to find an exact max-cut (enough to learn the entire graph).
Cite as

Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg. On the Cut-Query Complexity of Approximating Max-Cut. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{plevrakis_et_al:LIPIcs.ICALP.2024.115,
  author =	{Plevrakis, Orestis and Ragavan, Seyoon and Weinberg, S. Matthew},
  title =	{{On the Cut-Query Complexity of Approximating Max-Cut}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{115:1--115:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.115},
  URN =		{urn:nbn:de:0030-drops-202587},
  doi =		{10.4230/LIPIcs.ICALP.2024.115},
  annote =	{Keywords: query complexity, maximum cut, approximation algorithms, graph sparsification}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2024.2
The Role of Local Algorithms in Privacy (Invited Talk)

Authors: Sofya Raskhodnikova

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
We will discuss research areas at the intersection of local algorithms and differential privacy. The main focus will be on using local Lipschitz filters to enable black-box differentially private queries to sensitive datasets. We will also cover new sublinear computational tasks arising in private data analysis. Finally, we will touch upon distributed models of privacy.
Cite as

Sofya Raskhodnikova. The Role of Local Algorithms in Privacy (Invited Talk). In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{raskhodnikova:LIPIcs.STACS.2024.2,
  author =	{Raskhodnikova, Sofya},
  title =	{{The Role of Local Algorithms in Privacy}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.2},
  URN =		{urn:nbn:de:0030-drops-197123},
  doi =		{10.4230/LIPIcs.STACS.2024.2},
  annote =	{Keywords: Sublinear algorithms, differential privacy, reconstruction of Lipschitz functions, local algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.11
Property Testing with Online Adversaries

Authors: Omri Ben-Eliezer, Esty Kelman, Uri Meir, and Sofya Raskhodnikova

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

Abstract
The online manipulation-resilient testing model, proposed by Kalemaj, Raskhodnikova and Varma (ITCS 2022 and Theory of Computing 2023), studies property testing in situations where access to the input degrades continuously and adversarially. Specifically, after each query made by the tester is answered, the adversary can intervene and either erase or corrupt t data points. In this work, we investigate a more nuanced version of the online model in order to overcome old and new impossibility results for the original model. We start by presenting an optimal tester for linearity and a lower bound for low-degree testing of Boolean functions in the original model. We overcome the lower bound by allowing batch queries, where the tester gets a group of queries answered between manipulations of the data. Our batch size is small enough so that function values for a single batch on their own give no information about whether the function is of low degree. Finally, to overcome the impossibility results of Kalemaj et al. for sortedness and the Lipschitz property of sequences, we extend the model to include t < 1, i.e., adversaries that make less than one erasure per query. For sortedness, we characterize the rate of erasures for which online testing can be performed, exhibiting a sharp transition from optimal query complexity to impossibility of testability (with any number of queries). Our online tester works for a general class of local properties of sequences. One feature of our results is that we get new (and in some cases, simpler) optimal algorithms for several properties in the standard property testing model.
Cite as

Omri Ben-Eliezer, Esty Kelman, Uri Meir, and Sofya Raskhodnikova. Property Testing with Online Adversaries. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beneliezer_et_al:LIPIcs.ITCS.2024.11,
  author =	{Ben-Eliezer, Omri and Kelman, Esty and Meir, Uri and Raskhodnikova, Sofya},
  title =	{{Property Testing with Online Adversaries}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{11:1--11:25},
  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.2024.11},
  URN =		{urn:nbn:de:0030-drops-195395},
  doi =		{10.4230/LIPIcs.ITCS.2024.11},
  annote =	{Keywords: Linearity testing, low-degree testing, Reed-Muller codes, testing properties of sequences, erasure-resilience, corruption-resilience}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.66
Testing Connectedness of Images

Authors: Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova, and Dragos Ristache

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We investigate algorithms for testing whether an image is connected. Given a proximity parameter ε ∈ (0,1) and query access to a black-and-white image represented by an n×n matrix of Boolean pixel values, a (1-sided error) connectedness tester accepts if the image is connected and rejects with probability at least 2/3 if the image is ε-far from connected. We show that connectedness can be tested nonadaptively with O(1/ε²) queries and adaptively with O(1/ε^{3/2} √{log1/ε}) queries. The best connectedness tester to date, by Berman, Raskhodnikova, and Yaroslavtsev (STOC 2014) had query complexity O(1/ε² log 1/ε) and was adaptive. We also prove that every nonadaptive, 1-sided error tester for connectedness must make Ω(1/ε log 1/ε) queries.
Cite as

Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova, and Dragos Ristache. Testing Connectedness of Images. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berman_et_al:LIPIcs.APPROX/RANDOM.2023.66,
  author =	{Berman, Piotr and Murzabulatov, Meiram and Raskhodnikova, Sofya and Ristache, Dragos},
  title =	{{Testing Connectedness of Images}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.66},
  URN =		{urn:nbn:de:0030-drops-188918},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.66},
  annote =	{Keywords: Property testing, sublinear-algorithms, lower bounds, connectivity, graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.25
Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing

Authors: Hadley Black, Iden Kalemaj, and Sofya Raskhodnikova

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

Abstract
We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions f:{0,1}^d → ℝ. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function f over an arbitrary partially ordered domain as a collection of Boolean functions over the same domain, roughly capturing the distance of f to monotonicity and the structure of violations of f to monotonicity. We apply our generalized isoperimetric inequality to improve algorithms for testing monotonicity and approximating the distance to monotonicity for real-valued functions. Our tester for monotonicity has query complexity Õ(min(r √d,d)), where r is the size of the image of the input function. (The best previously known tester makes O(d) queries, as shown by Chakrabarty and Seshadhri (STOC 2013).) Our tester is nonadaptive and has 1-sided error. We prove a matching lower bound for nonadaptive, 1-sided error testers for monotonicity. We also show that the distance to monotonicity of real-valued functions that are α-far from monotone can be approximated nonadaptively within a factor of O(√{d log d}) with query complexity polynomial in 1/α and the dimension d. This query complexity is known to be nearly optimal for nonadaptive algorithms even for the special case of Boolean functions. (The best previously known distance approximation algorithm for real-valued functions, by Fattal and Ron (TALG 2010) achieves O(d log r)-approximation.)
Cite as

Hadley Black, Iden Kalemaj, and Sofya Raskhodnikova. Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{black_et_al:LIPIcs.ICALP.2023.25,
  author =	{Black, Hadley and Kalemaj, Iden and Raskhodnikova, Sofya},
  title =	{{Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{25:1--25:20},
  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.2023.25},
  URN =		{urn:nbn:de:0030-drops-180774},
  doi =		{10.4230/LIPIcs.ICALP.2023.25},
  annote =	{Keywords: Isoperimetric inequalities, property testing, monotonicity testing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.52
Triangle Counting with Local Edge Differential Privacy

Authors: Talya Eden, Quanquan C. Liu, Sofya Raskhodnikova, and Adam Smith

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

Abstract
Many deployments of differential privacy in industry are in the local model, where each party releases its private information via a differentially private randomizer. We study triangle counting in the noninteractive and interactive local model with edge differential privacy (that, intuitively, requires that the outputs of the algorithm on graphs that differ in one edge be indistinguishable). In this model, each party’s local view consists of the adjacency list of one vertex. In the noninteractive model, we prove that additive Ω(n²) error is necessary, where n is the number of nodes. This lower bound is our main technical contribution. It uses a reconstruction attack with a new class of linear queries and a novel mix-and-match strategy of running the local randomizers with different completions of their adjacency lists. It matches the additive error of the algorithm based on Randomized Response, proposed by Imola, Murakami and Chaudhuri (USENIX2021) and analyzed by Imola, Murakami and Chaudhuri (CCS2022) for constant ε. We use a different postprocessing of Randomized Response and provide tight bounds on the variance of the resulting algorithm. In the interactive setting, we prove a lower bound of Ω(n^{3/2}) on the additive error. Previously, no hardness results were known for interactive, edge-private algorithms in the local model, except for those that follow trivially from the results for the central model. Our work significantly improves on the state of the art in differentially private graph analysis in the local model.
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Talya Eden, Quanquan C. Liu, Sofya Raskhodnikova, and Adam Smith. Triangle Counting with Local Edge Differential Privacy. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 52:1-52:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{eden_et_al:LIPIcs.ICALP.2023.52,
  author =	{Eden, Talya and Liu, Quanquan C. and Raskhodnikova, Sofya and Smith, Adam},
  title =	{{Triangle Counting with Local Edge Differential Privacy}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{52:1--52:21},
  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.2023.52},
  URN =		{urn:nbn:de:0030-drops-181048},
  doi =		{10.4230/LIPIcs.ICALP.2023.52},
  annote =	{Keywords: local differential privacy, reconstruction attacks, lower bounds, triangle counting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.90
Sublinear-Time Computation in the Presence of Online Erasures

Authors: Iden Kalemaj, Sofya Raskhodnikova, and Nithin Varma

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

Abstract
We initiate the study of sublinear-time algorithms that access their input via an online adversarial erasure oracle. After answering each query to the input object, such an oracle can erase t input values. Our goal is to understand the complexity of basic computational tasks in extremely adversarial situations, where the algorithm’s access to data is blocked during the execution of the algorithm in response to its actions. Specifically, we focus on property testing in the model with online erasures. We show that two fundamental properties of functions, linearity and quadraticity, can be tested for constant t with asymptotically the same complexity as in the standard property testing model. For linearity testing, we prove tight bounds in terms of t, showing that the query complexity is Θ(log t). In contrast to linearity and quadraticity, some other properties, including sortedness and the Lipschitz property of sequences, cannot be tested at all, even for t = 1. Our investigation leads to a deeper understanding of the structure of violations of linearity and other widely studied properties.
Cite as

Iden Kalemaj, Sofya Raskhodnikova, and Nithin Varma. Sublinear-Time Computation in the Presence of Online Erasures. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 90:1-90:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kalemaj_et_al:LIPIcs.ITCS.2022.90,
  author =	{Kalemaj, Iden and Raskhodnikova, Sofya and Varma, Nithin},
  title =	{{Sublinear-Time Computation in the Presence of Online Erasures}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{90:1--90:25},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.90},
  URN =		{urn:nbn:de:0030-drops-156867},
  doi =		{10.4230/LIPIcs.ITCS.2022.90},
  annote =	{Keywords: Randomized algorithms, property testing, Fourier analysis, linear functions, quadratic functions, Lipschitz and monotone functions, sorted sequences}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.80
Erasure-Resilient Sublinear-Time Graph Algorithms

Authors: Amit Levi, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and Nithin Varma

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial erasures in adjacency entries. We focus on two computational tasks: testing if a graph is connected or ε-far from connected and estimating the average degree. For testing connectedness, we discover a threshold phenomenon: when the fraction of erasures is less than ε, this property can be tested efficiently (in time independent of the size of the graph); when the fraction of erasures is at least ε, then a number of queries linear in the size of the graph representation is required. Our erasure-resilient algorithm (for the special case with no erasures) is an improvement over the previously known algorithm for connectedness in the standard property testing model and has optimal dependence on the proximity parameter ε. For estimating the average degree, our results provide an "interpolation" between the query complexity for this computational task in the model with no erasures in two different settings: with only degree queries, investigated by Feige (SIAM J. Comput. `06), and with degree queries and neighbor queries, investigated by Goldreich and Ron (Random Struct. Algorithms `08) and Eden et al. (ICALP `17). We conclude with a discussion of our model and open questions raised by our work.
Cite as

Amit Levi, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and Nithin Varma. Erasure-Resilient Sublinear-Time Graph Algorithms. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 80:1-80:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{levi_et_al:LIPIcs.ITCS.2021.80,
  author =	{Levi, Amit and Pallavoor, Ramesh Krishnan S. and Raskhodnikova, Sofya and Varma, Nithin},
  title =	{{Erasure-Resilient Sublinear-Time Graph Algorithms}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{80:1--80:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.80},
  URN =		{urn:nbn:de:0030-drops-136192},
  doi =		{10.4230/LIPIcs.ITCS.2021.80},
  annote =	{Keywords: Graph property testing, Computing with incomplete information, Approximating graph parameters}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.63
Erasures vs. Errors in Local Decoding and Property Testing

Authors: Sofya Raskhodnikova, Noga Ron-Zewi, and Nithin Varma

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures. Motivated by applications in property testing, we begin our investigation with local list decoding in the presence of erasures. We prove an analog of a famous result of Goldreich and Levin on local list decodability of the Hadamard code. Specifically, we show that the Hadamard code is locally list decodable in the presence of a constant fraction of erasures, arbitrary close to 1, with list sizes and query complexity better than in the Goldreich-Levin theorem. We use this result to exhibit a property which is testable with a number of queries independent of the length of the input in the presence of erasures, but requires a number of queries that depends on the input length, n, for tolerant testing. We further study approximate locally list decodable codes that work against erasures and use them to strengthen our separation by constructing a property which is testable with a constant number of queries in the presence of erasures, but requires n^{Omega(1)} queries for tolerant testing. Next, we study the general relationship between local decoding in the presence of errors and in the presence of erasures. We observe that every locally (uniquely or list) decodable code that works in the presence of errors also works in the presence of twice as many erasures (with the same parameters up to constant factors). We show that there is also an implication in the other direction for locally decodable codes (with unique decoding): specifically, that the existence of a locally decodable code that works in the presence of erasures implies the existence of a locally decodable code that works in the presence of errors and has related parameters. However, it remains open whether there is an implication in the other direction for locally list decodable codes. We relate this question to other open questions in local decoding.
Cite as

Sofya Raskhodnikova, Noga Ron-Zewi, and Nithin Varma. Erasures vs. Errors in Local Decoding and Property Testing. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 63:1-63:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{raskhodnikova_et_al:LIPIcs.ITCS.2019.63,
  author =	{Raskhodnikova, Sofya and Ron-Zewi, Noga and Varma, Nithin},
  title =	{{Erasures vs. Errors in Local Decoding and Property Testing}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{63:1--63:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.63},
  URN =		{urn:nbn:de:0030-drops-101568},
  doi =		{10.4230/LIPIcs.ITCS.2019.63},
  annote =	{Keywords: Error-correcting codes, probabilistically checkable proofs (PCPs) of proximity, Hadamard code, local list decoding, tolerant testing}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.111
Brief Announcement: Erasure-Resilience Versus Tolerance to Errors

Authors: Sofya Raskhodnikova and Nithin Varma

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We describe work in progress on providing a separation between erasure-resilient and tolerant property testing. Specifically, we are able to exhibit a property which is testable (with the number of queries independent of the length of the input) in the presence of erasures, but is not testable tolerantly.
Cite as

Sofya Raskhodnikova and Nithin Varma. Brief Announcement: Erasure-Resilience Versus Tolerance to Errors. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 111:1-111:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{raskhodnikova_et_al:LIPIcs.ICALP.2018.111,
  author =	{Raskhodnikova, Sofya and Varma, Nithin},
  title =	{{Brief Announcement: Erasure-Resilience Versus Tolerance to Errors}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{111:1--111:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.111},
  URN =		{urn:nbn:de:0030-drops-91154},
  doi =		{10.4230/LIPIcs.ICALP.2018.111},
  annote =	{Keywords: Property testing, erasures, tolerance to errors, model separation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.12
Parameterized Property Testing of Functions

Authors: Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and Nithin Varma

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
We investigate the parameters in terms of which the complexity of sublinear-time algorithms should be expressed. Our goal is to find input parameters that are tailored to the combinatorics of the specific problem being studied and design algorithms that run faster when these parameters are small. This direction enables us to surpass the (worst-case) lower bounds, expressed in terms of the input size, for several problems. Our aim is to develop a similar level of understanding of the complexity of sublinear-time algorithms to the one that was enabled by research in parameterized complexity for classical algorithms. Specifically, we focus on testing properties of functions. By parameterizing the query complexity in terms of the size r of the image of the input function, we obtain testers for monotonicity and convexity of functions of the form f:[n]\to \mathbb{R} with query complexity O(\log r), with no dependence on n. The result for monotonicity circumvents the \Omega(\log n) lower bound by Fischer (Inf. Comput., 2004) for this problem. We present several other parameterized testers, providing compelling evidence that expressing the query complexity of property testers in terms of the input size is not always the best choice.
Cite as

Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and Nithin Varma. Parameterized Property Testing of Functions. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pallavoor_et_al:LIPIcs.ITCS.2017.12,
  author =	{Pallavoor, Ramesh Krishnan S. and Raskhodnikova, Sofya and Varma, Nithin},
  title =	{{Parameterized Property Testing of Functions}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.12},
  URN =		{urn:nbn:de:0030-drops-81479},
  doi =		{10.4230/LIPIcs.ITCS.2017.12},
  annote =	{Keywords: Sublinear algorithms, property testing, parameterization, monotonicity, convexity}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.5
Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

Authors: Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We study the problem of testing unateness of functions f:{0,1}^d -> R. We give an O(d/\epsilon . log(d/\epsilon))-query nonadaptive tester and an O(d/\epsilon)-query adaptive tester and show that both testers are optimal for a fixed distance parameter \epsilon. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover, no lower bounds for testing unateness were known. We generalize our results to obtain optimal unateness testers for functions f:[n]^d -> R. Our results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form {0,1}^d and, more generally, [n]^d. This stands in contrast to the situation for monotonicity testing where there is no adaptivity gap for functions f:[n]^d -> R.
Cite as

Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri. Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{baleshzar_et_al:LIPIcs.ICALP.2017.5,
  author =	{Baleshzar, Roksana and Chakrabarty, Deeparnab and Pallavoor, Ramesh Krishnan S. and Raskhodnikova, Sofya and Seshadhri, C.},
  title =	{{Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.5},
  URN =		{urn:nbn:de:0030-drops-74844},
  doi =		{10.4230/LIPIcs.ICALP.2017.5},
  annote =	{Keywords: Property testing, unate and monotone functions}
}
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