10 Search Results for "Ben-Eliezer, Omri"

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-dev.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
DOI: 10.4230/LIPIcs.ITCS.2023.15
Is This Correct? Let’s Check!

Authors: Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, and Madhu Sudan

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

Abstract
Societal accumulation of knowledge is a complex process. The correctness of new units of knowledge depends not only on the correctness of new reasoning, but also on the correctness of old units that the new one builds on. The errors in such accumulation processes are often remedied by error correction and detection heuristics. Motivating examples include the scientific process based on scientific publications, and software development based on libraries of code. Natural processes that aim to keep errors under control, such as peer review in scientific publications, and testing and debugging in software development, would typically check existing pieces of knowledge - both for the reasoning that generated them and the previous facts they rely on. In this work, we present a simple process that models such accumulation of knowledge and study the persistence (or lack thereof) of errors. We consider a simple probabilistic model for the generation of new units of knowledge based on the preferential attachment growth model, which additionally allows for errors. Furthermore, the process includes checks aimed at catching these errors. We investigate when effects of errors persist forever in the system (with positive probability) and when they get rooted out completely by the checking process. The two basic parameters associated with the checking process are the probability of conducting a check and the depth of the check. We show that errors are rooted out if checks are sufficiently frequent and sufficiently deep. In contrast, shallow or infrequent checks are insufficient to root out errors.
Cite as

Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, and Madhu Sudan. Is This Correct? Let’s Check!. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{beneliezer_et_al:LIPIcs.ITCS.2023.15,
  author =	{Ben-Eliezer, Omri and Mikulincer, Dan and Mossel, Elchanan and Sudan, Madhu},
  title =	{{Is This Correct? Let’s Check!}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{15:1--15:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.15},
  URN =		{urn:nbn:de:0030-drops-175180},
  doi =		{10.4230/LIPIcs.ITCS.2023.15},
  annote =	{Keywords: Error Propagation, Preferential Attachment}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.17
Finding Monotone Patterns in Sublinear Time, Adaptively

Authors: Omri Ben-Eliezer, Shoham Letzter, and Erik Waingarten

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

Abstract
We investigate adaptive sublinear algorithms for finding monotone patterns in sequential data. Given fixed 2 ≤ k ∈ m N and ε > 0, consider the problem of finding a length-k increasing subsequence in a sequence f : [n] → ℝ, provided that f is ε-far from free of such subsequences. It was shown by Ben-Eliezer et al. [FOCS 2019] that the non-adaptive query complexity of the above task is Θ((log n)^⌊log₂ k⌋). In this work, we break the non-adaptive lower bound, presenting an adaptive algorithm for this problem which makes O(log n) queries. This is optimal, matching the classical Ω(log n) adaptive lower bound by Fischer [Inf. Comp. 2004] for monotonicity testing (which corresponds to the case k = 2). Equivalently, our result implies that testing whether a sequence decomposes into k monotone subsequences can be done with O(log n) queries.
Cite as

Omri Ben-Eliezer, Shoham Letzter, and Erik Waingarten. Finding Monotone Patterns in Sublinear Time, Adaptively. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2022.17,
  author =	{Ben-Eliezer, Omri and Letzter, Shoham and Waingarten, Erik},
  title =	{{Finding Monotone Patterns in Sublinear Time, Adaptively}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.17},
  URN =		{urn:nbn:de:0030-drops-163586},
  doi =		{10.4230/LIPIcs.ICALP.2022.17},
  annote =	{Keywords: property testing, monotone patterns, monotone decomposition, adaptivity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.98
Strongly Sublinear Algorithms for Testing Pattern Freeness

Authors: Ilan Newman and Nithin Varma

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

Abstract
For a permutation π:[k] → [k], a function f:[n] → ℝ contains a π-appearance if there exists 1 ≤ i₁ < i₂ < … < i_k ≤ n such that for all s,t ∈ [k], f(i_s) < f(i_t) if and only if π(s) < π(t). The function is π-free if it has no π-appearances. In this paper, we investigate the problem of testing whether an input function f is π-free or whether f differs on at least ε n values from every π-free function. This is a generalization of the well-studied monotonicity testing and was first studied by Newman, Rabinovich, Rajendraprasad and Sohler [Ilan Newman et al., 2019]. We show that for all constants k ∈ ℕ, ε ∈ (0,1), and permutation π:[k] → [k], there is a one-sided error ε-testing algorithm for π-freeness of functions f:[n] → ℝ that makes Õ(n^o(1)) queries. We improve significantly upon the previous best upper bound O(n^{1 - 1/(k-1)}) by Ben-Eliezer and Canonne [Omri Ben-Eliezer and Clément L. Canonne, 2018]. Our algorithm is adaptive, while the earlier best upper bound is known to be tight for nonadaptive algorithms.
Cite as

Ilan Newman and Nithin Varma. Strongly Sublinear Algorithms for Testing Pattern Freeness. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 98:1-98:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{newman_et_al:LIPIcs.ICALP.2022.98,
  author =	{Newman, Ilan and Varma, Nithin},
  title =	{{Strongly Sublinear Algorithms for Testing Pattern Freeness}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{98:1--98:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.98},
  URN =		{urn:nbn:de:0030-drops-164390},
  doi =		{10.4230/LIPIcs.ICALP.2022.98},
  annote =	{Keywords: Property testing, Pattern freeness, Sublinear algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.42
Ordered Graph Limits and Their Applications

Authors: Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Yuichi Yoshida

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

Abstract
The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in analytic language. We extend the theory of graph limits to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which we call an orderon. As a special case, this yields limit objects for matrices whose rows and columns are ordered, and for dynamic graphs that expand (via vertex insertions) over time. Along the way, we devise an ordered locality-preserving variant of the cut distance between ordered graphs, showing that two graphs are close with respect to this distance if and only if they are similar in terms of their ordered subgraph frequencies. We show that the space of orderons is compact with respect to this distance notion, which is key to a successful analysis of combinatorial objects through their limits. For the proof we combine techniques used in the unordered setting with several new techniques specifically designed to overcome the challenges arising in the ordered setting. We derive several applications of the ordered limit theory in extremal combinatorics, sampling, and property testing in ordered graphs. In particular, we prove a new ordered analogue of the well-known result by Alon and Stav [RS&A'08] on the furthest graph from a hereditary property; this is the first known result of this type in the ordered setting. Unlike the unordered regime, here the Erdős–Rényi random graph 𝐆(n, p) with an ordering over the vertices is not always asymptotically the furthest from the property for some p. However, using our ordered limit theory, we show that random graphs generated by a stochastic block model, where the blocks are consecutive in the vertex ordering, are (approximately) the furthest. Additionally, we describe an alternative analytic proof of the ordered graph removal lemma [Alon et al., FOCS'17].
Cite as

Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Yuichi Yoshida. Ordered Graph Limits and Their Applications. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{beneliezer_et_al:LIPIcs.ITCS.2021.42,
  author =	{Ben-Eliezer, Omri and Fischer, Eldar and Levi, Amit and Yoshida, Yuichi},
  title =	{{Ordered Graph Limits and Their Applications}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{42:1--42:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.42},
  URN =		{urn:nbn:de:0030-drops-135815},
  doi =		{10.4230/LIPIcs.ITCS.2021.42},
  annote =	{Keywords: graph limits, ordered graph, graphon, cut distance, removal lemma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.9
Hard Properties with (Very) Short PCPPs and Their Applications

Authors: Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Ron D. Rothblum

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed ℓ, we construct a property P^(ℓ)⊆ {0,1}^n satisfying the following: Any testing algorithm for P^(ℓ) requires Ω(n) many queries, and yet P^(ℓ) has a constant query PCPP whose proof size is O(n⋅log^(ℓ)n), where log^(ℓ) denotes the ℓ times iterated log function (e.g., log^(2)n = log log n). The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n⋅polylog(n)). As an immediate application, we obtain stronger separations between the standard testing model and both the tolerant testing model and the erasure-resilient testing model: for every fixed ℓ, we construct a property that has a constant-query tester, but requires Ω(n/log^(ℓ)(n)) queries for every tolerant or erasure-resilient tester.
Cite as

Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Ron D. Rothblum. Hard Properties with (Very) Short PCPPs and Their Applications. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 9:1-9:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{beneliezer_et_al:LIPIcs.ITCS.2020.9,
  author =	{Ben-Eliezer, Omri and Fischer, Eldar and Levi, Amit and Rothblum, Ron D.},
  title =	{{Hard Properties with (Very) Short PCPPs and Their Applications}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{9:1--9:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.9},
  URN =		{urn:nbn:de:0030-drops-116949},
  doi =		{10.4230/LIPIcs.ITCS.2020.9},
  annote =	{Keywords: PCPP, Property testing, Tolerant testing, Erasure resilient testing, Randomized encoding, Coding theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.11
Testing Local Properties of Arrays

Authors: Omri Ben-Eliezer

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

Abstract
We study testing of local properties in one-dimensional and multi-dimensional arrays. A property of d-dimensional arrays f:[n]^d -> Sigma is k-local if it can be defined by a family of k x ... x k forbidden consecutive patterns. This definition captures numerous interesting properties. For example, monotonicity, Lipschitz continuity and submodularity are 2-local; convexity is (usually) 3-local; and many typical problems in computational biology and computer vision involve o(n)-local properties. In this work, we present a generic approach to test all local properties of arrays over any finite (and not necessarily bounded size) alphabet. We show that any k-local property of d-dimensional arrays is testable by a simple canonical one-sided error non-adaptive epsilon-test, whose query complexity is O(epsilon^{-1}k log{(epsilon n)/k}) for d = 1 and O(c_d epsilon^{-1/d} k * n^{d-1}) for d > 1. The queries made by the canonical test constitute sphere-like structures of varying sizes, and are completely independent of the property and the alphabet Sigma. The query complexity is optimal for a wide range of parameters: For d=1, this matches the query complexity of many previously investigated local properties, while for d > 1 we design and analyze new constructions of k-local properties whose one-sided non-adaptive query complexity matches our upper bounds. For some previously studied properties, our method provides the first known sublinear upper bound on the query complexity.
Cite as

Omri Ben-Eliezer. Testing Local Properties of Arrays. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{beneliezer:LIPIcs.ITCS.2019.11,
  author =	{Ben-Eliezer, Omri},
  title =	{{Testing Local Properties of Arrays}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{11:1--11:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.11},
  URN =		{urn:nbn:de:0030-drops-101041},
  doi =		{10.4230/LIPIcs.ITCS.2019.11},
  annote =	{Keywords: Property Testing, Local Properties, Monotonicity Testing, Hypergrid, Pattern Matching}
}
Document
DOI: 10.4230/LIPIcs.CCC.2018.18
Earthmover Resilience and Testing in Ordered Structures

Authors: Omri Ben-Eliezer and Eldar Fischer

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Abstract
One of the main challenges in property testing is to characterize those properties that are testable with a constant number of queries. For unordered structures such as graphs and hypergraphs this task has been mostly settled. However, for ordered structures such as strings, images, and ordered graphs, the characterization problem seems very difficult in general. In this paper, we identify a wide class of properties of ordered structures - the earthmover resilient (ER) properties - and show that the "good behavior" of such properties allows us to obtain general testability results that are similar to (and more general than) those of unordered graphs. A property P is ER if, roughly speaking, slight changes in the order of the elements in an object satisfying P cannot make this object far from P. The class of ER properties includes, e.g., all unordered graph properties, many natural visual properties of images, such as convexity, and all hereditary properties of ordered graphs and images. A special case of our results implies, building on a recent result of Alon and the authors, that the distance of a given image or ordered graph from any hereditary property can be estimated (with good probability) up to a constant additive error, using a constant number of queries.
Cite as

Omri Ben-Eliezer and Eldar Fischer. Earthmover Resilience and Testing in Ordered Structures. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 18:1-18:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{beneliezer_et_al:LIPIcs.CCC.2018.18,
  author =	{Ben-Eliezer, Omri and Fischer, Eldar},
  title =	{{Earthmover Resilience and Testing in Ordered Structures}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{18:1--18:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.18},
  URN =		{urn:nbn:de:0030-drops-88718},
  doi =		{10.4230/LIPIcs.CCC.2018.18},
  annote =	{Keywords: characterizations of testability, distance estimation, earthmover resilient, ordered structures, property testing}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.25
Efficient Removal Lemmas for Matrices

Authors: Noga Alon and Omri Ben-Eliezer

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
The authors and Fischer recently proved that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a constant number of queries, by establishing an (ordered) matrix removal lemma, which states the following: If a matrix is far from satisfying some hereditary property, then a large enough constant-size random submatrix of it does not satisfy the property with probability at least 9/10. Here being far from the property means that one needs to modify a constant fraction of the entries of the matrix to make it satisfy the property. However, in the above general removal lemma, the required size of the random submatrix grows very fast as a function of the distance of the matrix from satisfying the property. In this work we establish much more efficient removal lemmas for several special cases of the above problem. In particular, we show the following: If an epsilon-fraction of the entries of a binary matrix M can be covered by pairwise-disjoint copies of some (s x t) matrix A, then a delta-fraction of the (s x t)-submatrices of M are equal to A, where delta is polynomial in epsilon. We generalize the work of Alon, Fischer and Newman [SICOMP'07] and make progress towards proving one of their conjectures. The proofs combine their efficient conditional regularity lemma for matrices with additional combinatorial and probabilistic ideas.
Cite as

Noga Alon and Omri Ben-Eliezer. Efficient Removal Lemmas for Matrices. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{alon_et_al:LIPIcs.APPROX-RANDOM.2017.25,
  author =	{Alon, Noga and Ben-Eliezer, Omri},
  title =	{{Efficient Removal Lemmas for Matrices}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.25},
  URN =		{urn:nbn:de:0030-drops-75744},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.25},
  annote =	{Keywords: Property Testing, Removal Lemma, Matrix Regularity Lemma, Binary Matrix}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.9
Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Authors: Omri Ben-Eliezer, Simon Korman, and Daniel Reichman

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

Abstract
Analyzing multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms to understand local properties of the data. We focus on the natural problem of testing pattern freeness: given a large d-dimensional array A and a fixed d-dimensional pattern P over a finite alphabet Gamma, we say that A is P-free if it does not contain a copy of the forbidden pattern P as a consecutive subarray. The distance of A to P-freeness is the fraction of the entries of A that need to be modified to make it P-free. For any epsilon > 0 and any large enough pattern P over any alphabet - other than a very small set of exceptional patterns - we design a tolerant tester that distinguishes between the case that the distance is at least epsilon and the case that the distance is at most a_d epsilon, with query complexity and running time c_d epsilon^{-1}, where a_d < 1 and c_d depend only on the dimension d. These testers only need to access uniformly random blocks of samples from the input A. To analyze the testers we establish several combinatorial results, including the following d-dimensional modification lemma, which might be of independent interest: For any large enough d-dimensional pattern P over any alphabet (excluding a small set of exceptional patterns for the binary case), and any d-dimensional array A containing a copy of P, one can delete this copy by modifying one of its locations without creating new P-copies in A. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data.
Cite as

Omri Ben-Eliezer, Simon Korman, and Daniel Reichman. Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2017.9,
  author =	{Ben-Eliezer, Omri and Korman, Simon and Reichman, Daniel},
  title =	{{Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{9:1--9:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.9},
  URN =		{urn:nbn:de:0030-drops-74427},
  doi =		{10.4230/LIPIcs.ICALP.2017.9},
  annote =	{Keywords: Property testing, Sublinear algorithms, Pattern matching}
}
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