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Documents authored by Ramnarayan, Govind

Document
DOI: 10.4230/LIPIcs.ITCS.2019.45
Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't

Authors: Yan Jin, Elchanan Mossel, and Govind Ramnarayan

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

Abstract
We consider a variation of the problem of corruption detection on networks posed by Alon, Mossel, and Pemantle '15. In this model, each vertex of a graph can be either truthful or corrupt. Each vertex reports about the types (truthful or corrupt) of all its neighbors to a central agency, where truthful nodes report the true types they see and corrupt nodes report adversarially. The central agency aggregates these reports and attempts to find a single truthful node. Inspired by real auditing networks, we pose our problem for arbitrary graphs and consider corruption through a computational lens. We identify a key combinatorial parameter of the graph m(G), which is the minimal number of corrupted agents needed to prevent the central agency from identifying a single corrupt node. We give an efficient (in fact, linear time) algorithm for the central agency to identify a truthful node that is successful whenever the number of corrupt nodes is less than m(G)/2. On the other hand, we prove that for any constant alpha > 1, it is NP-hard to find a subset of nodes S in G such that corrupting S prevents the central agency from finding one truthful node and |S| <= alpha m(G), assuming the Small Set Expansion Hypothesis (Raghavendra and Steurer, STOC '10). We conclude that being corrupt requires being clever, while detecting corruption does not. Our main technical insight is a relation between the minimum number of corrupt nodes required to hide all truthful nodes and a certain notion of vertex separability for the underlying graph. Additionally, this insight lets us design an efficient algorithm for a corrupt party to decide which graphs require the fewest corrupted nodes, up to a multiplicative factor of O(log n).
Cite as

Yan Jin, Elchanan Mossel, and Govind Ramnarayan. Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jin_et_al:LIPIcs.ITCS.2019.45,
  author =	{Jin, Yan and Mossel, Elchanan and Ramnarayan, Govind},
  title =	{{Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{45:1--45:14},
  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.2019.45},
  URN =		{urn:nbn:de:0030-drops-101388},
  doi =		{10.4230/LIPIcs.ITCS.2019.45},
  annote =	{Keywords: Corruption detection, PMC Model, Small Set Expansion, Hardness of Approximation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.27
Relaxed Locally Correctable Codes

Authors: Tom Gur, Govind Ramnarayan, and Ron D. Rothblum

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
Locally decodable codes (LDCs) and locally correctable codes (LCCs) are error-correcting codes in which individual bits of the message and codeword, respectively, can be recovered by querying only few bits from a noisy codeword. These codes have found numerous applications both in theory and in practice. A natural relaxation of LDCs, introduced by Ben-Sasson et al. (SICOMP, 2006), allows the decoder to reject (i.e., refuse to answer) in case it detects that the codeword is corrupt. They call such a decoder a relaxed decoder and construct a constant-query relaxed LDC with almost-linear blocklength, which is sub-exponentially better than what is known for (full-fledged) LDCs in the constant-query regime. We consider an analogous relaxation for local correction. Thus, a relaxed local corrector reads only few bits from a (possibly) corrupt codeword and either recovers the desired bit of the codeword, or rejects in case it detects a corruption. We give two constructions of relaxed LCCs in two regimes, where the first optimizes the query complexity and the second optimizes the rate: 1. Constant Query Complexity: A relaxed LCC with polynomial blocklength whose corrector only reads a constant number of bits of the codeword. This is a sub-exponential improvement over the best constant query (full-fledged) LCCs that are known. 2. Constant Rate: A relaxed LCC with constant rate (i.e., linear blocklength) with quasi-polylogarithmic query complexity. This is a nearly sub-exponential improvement over the query complexity of a recent (full-fledged) constant-rate LCC of Kopparty et al. (STOC, 2016).
Cite as

Tom Gur, Govind Ramnarayan, and Ron D. Rothblum. Relaxed Locally Correctable Codes. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 27:1-27:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gur_et_al:LIPIcs.ITCS.2018.27,
  author =	{Gur, Tom and Ramnarayan, Govind and Rothblum, Ron D.},
  title =	{{Relaxed Locally Correctable Codes}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{27:1--27:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.27},
  URN =		{urn:nbn:de:0030-drops-83154},
  doi =		{10.4230/LIPIcs.ITCS.2018.27},
  annote =	{Keywords: Keywords and phrases Coding Theory, Locally Correctable Codes, Probabilistically Checkable Proofs}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.42
A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian

Authors: Dana Moshkovitz, Govind Ramnarayan, and Henry Yuen

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
In this work we show a barrier towards proving a randomness-efficient parallel repetition, a promising avenue for achieving many tight inapproximability results. Feige and Kilian (STOC'95) proved an impossibility result for randomness-efficient parallel repetition for two prover games with small degree, i.e., when each prover has only few possibilities for the question of the other prover. In recent years, there have been indications that randomness-efficient parallel repetition (also called derandomized parallel repetition) might be possible for games with large degree, circumventing the impossibility result of Feige and Kilian. In particular, Dinur and Meir (CCC'11) construct games with large degree whose repetition can be derandomized using a theorem of Impagliazzo, Kabanets and Wigderson (SICOMP'12). However, obtaining derandomized parallel repetition theorems that would yield optimal inapproximability results has remained elusive. This paper presents an explanation for the current impasse in progress, by proving a limitation on derandomized parallel repetition. We formalize two properties which we call "fortification-friendliness" and "yields robust embeddings". We show that any proof of derandomized parallel repetition achieving almost-linear blow-up cannot both (a) be fortification-friendly and (b) yield robust embeddings. Unlike Feige and Kilian, we do not require the small degree assumption. Given that virtually all existing proofs of parallel repetition, including the derandomized parallel repetition result of Dinur and Meir, share these two properties, our no-go theorem highlights a major barrier to achieving almost-linear derandomized parallel repetition.
Cite as

Dana Moshkovitz, Govind Ramnarayan, and Henry Yuen. A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 42:1-42:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{moshkovitz_et_al:LIPIcs.APPROX-RANDOM.2016.42,
  author =	{Moshkovitz, Dana and Ramnarayan, Govind and Yuen, Henry},
  title =	{{A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{42:1--42:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.42},
  URN =		{urn:nbn:de:0030-drops-66657},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.42},
  annote =	{Keywords: Derandomization, parallel repetition, Feige-Killian, fortification}
}
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