7 Search Results for "Pallavoor, Ramesh Krishnan S."

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.42
On the Spectral Expansion of Monotone Subsets of the Hypercube

Authors: Yumou Fei and Renato Ferreira Pinto Jr.

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset A ⊆ {0,1}ⁿ of density μ(A), the previous best lower bound on the spectral gap, due to Cohen [Cohen, 2016], was γ ≳ μ(A)/n², improving upon the earlier bound γ ≳ μ(A)²/n² established by Ding and Mossel [Ding and Mossel, 2014]. In this paper, we prove the optimal lower bound γ ≳ μ(A)/n. As a corollary, we improve the mixing time upper bound of the random walk on constant-density monotone sets from O(n³), as shown by Ding and Mossel, to O(n²). Along the way, we develop two new inequalities that may be of independent interest: (1) a directed L²-Poincaré inequality on the hypercube, and (2) an "approximate" FKG inequality for monotone sets.
Cite as

Yumou Fei and Renato Ferreira Pinto Jr.. On the Spectral Expansion of Monotone Subsets of the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 42:1-42:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fei_et_al:LIPIcs.APPROX/RANDOM.2025.42,
  author =	{Fei, Yumou and Ferreira Pinto Jr., Renato},
  title =	{{On the Spectral Expansion of Monotone Subsets of the Hypercube}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{42:1--42:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  URN =		{urn:nbn:de:0030-drops-244081},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  annote =	{Keywords: Random walks, mixing time, FKG inequality, Poincar\'{e} inequality, directed isoperimetry}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2025.2
Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation (Invited Talk)

Authors: Dana Ron

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

Abstract
This short paper accompanies an invited talk given at ICALP2025. It is an informal, high-level presentation of tolerant testing and distance approximation. It includes some general results as well as a few specific ones, with the aim of providing a taste of this research direction within the area of sublinear algorithms.
Cite as

Dana Ron. Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation (Invited Talk). In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ron:LIPIcs.ICALP.2025.2,
  author =	{Ron, Dana},
  title =	{{Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.2},
  URN =		{urn:nbn:de:0030-drops-233798},
  doi =		{10.4230/LIPIcs.ICALP.2025.2},
  annote =	{Keywords: Sublinear Algorithms, Tolerant Property Testing, Distance Approximation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.34
Directed Hypercube Routing, a Generalized Lehman-Ron Theorem, and Monotonicity Testing

Authors: Deeparnab Chakrabarty and C. Seshadhri

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Motivated by applications to monotonicity testing, Lehman and Ron (JCTA, 2001) proved the existence of a collection of vertex disjoint paths between comparable sub-level sets in the directed hypercube. The main technical contribution of this paper is a new proof method that yields a generalization of their theorem: we prove the existence of two edge-disjoint collections of vertex disjoint paths. Our main conceptual contributions are conjectures on directed hypercube flows with simultaneous vertex and edge capacities of which our generalized Lehman-Ron theorem is a special case. We show that these conjectures imply directed isoperimetric theorems, and in particular, the robust directed Talagrand inequality due to Khot, Minzer, and Safra (SIAM J. on Comp, 2018). These isoperimetric inequalities, that relate the directed surface area (of a set in the hypercube) to its distance to monotonicity, have been crucial in obtaining the best monotonicity testers for Boolean functions. We believe our conjectures pave the way towards combinatorial proofs of these directed isoperimetry theorems.
Cite as

Deeparnab Chakrabarty and C. Seshadhri. Directed Hypercube Routing, a Generalized Lehman-Ron Theorem, and Monotonicity Testing. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chakrabarty_et_al:LIPIcs.ITCS.2025.34,
  author =	{Chakrabarty, Deeparnab and Seshadhri, C.},
  title =	{{Directed Hypercube Routing, a Generalized Lehman-Ron Theorem, and Monotonicity Testing}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.34},
  URN =		{urn:nbn:de:0030-drops-226623},
  doi =		{10.4230/LIPIcs.ITCS.2025.34},
  annote =	{Keywords: Monotonicity testing, isoperimetric inequalities, hypercube routing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.65
Online Versus Offline Adversaries in Property Testing

Authors: Esty Kelman, Ephraim Linder, and Sofya Raskhodnikova

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We study property testing with incomplete or noisy inputs. The models we consider allow for adversarial manipulation of the input, but differ in whether the manipulation can be done only offline, i.e., before the execution of the algorithm, or online, i.e., as the algorithm runs. The manipulations by an adversary can come in the form of erasures or corruptions. We compare the query complexity and the randomness complexity of property testing in the offline and online models. Kalemaj, Raskhodnikova, and Varma (Theory Comput. `23) provide properties that can be tested with a small number of queries with offline erasures, but cannot be tested at all with online erasures. We demonstrate that the two models are incomparable in terms of query complexity: we construct properties that can be tested with a constant number of queries in the online corruption model, but require querying a significant fraction of the input in the offline erasure model. We also construct properties that exhibit a strong separation between the randomness complexity of testing in the presence of offline and online adversaries: testing these properties in the online model requires exponentially more random bits than in the offline model, even when they are tested with nearly the same number of queries in both models. Our randomness separation relies on a novel reduction from randomness-efficient testers in the adversarial online model to query-efficient testers in the standard model.
Cite as

Esty Kelman, Ephraim Linder, and Sofya Raskhodnikova. Online Versus Offline Adversaries in Property Testing. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kelman_et_al:LIPIcs.ITCS.2025.65,
  author =	{Kelman, Esty and Linder, Ephraim and Raskhodnikova, Sofya},
  title =	{{Online Versus Offline Adversaries in Property Testing}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{65:1--65:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.65},
  URN =		{urn:nbn:de:0030-drops-226933},
  doi =		{10.4230/LIPIcs.ITCS.2025.65},
  annote =	{Keywords: Property Testing, Online Adversary, Offline Adversary, Query Complexity, Randomness Complexity, Separations}
}
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.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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