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Documents authored by Gandikota, Venkata

Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.106
Brief Announcement: Relaxed Locally Correctable Codes in Computationally Bounded Channels

Authors: Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, and Samson Zhou

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

Abstract
We study variants of locally decodable and locally correctable codes in computationally bounded, adversarial channels, under the assumption that collision-resistant hash functions exist, and with no public-key or private-key cryptographic setup. Specifically, we provide constructions of relaxed locally correctable and relaxed locally decodable codes over the binary alphabet, with constant information rate, and poly-logarithmic locality. Our constructions compare favorably with existing schemes built under much stronger cryptographic assumptions, and with their classical analogues in the computationally unbounded, Hamming channel. Our constructions crucially employ collision-resistant hash functions and local expander graphs, extending ideas from recent cryptographic constructions of memory-hard functions.
Cite as

Jeremiah Blocki, Venkata Gandikota, Elena Grigorescu, and Samson Zhou. Brief Announcement: Relaxed Locally Correctable Codes in Computationally Bounded Channels. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 106:1-106:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{blocki_et_al:LIPIcs.ICALP.2018.106,
  author =	{Blocki, Jeremiah and Gandikota, Venkata and Grigorescu, Elena and Zhou, Samson},
  title =	{{Brief Announcement: Relaxed Locally Correctable Codes in Computationally Bounded Channels}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{106:1--106:4},
  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.2018.106},
  URN =		{urn:nbn:de:0030-drops-91102},
  doi =		{10.4230/LIPIcs.ICALP.2018.106},
  annote =	{Keywords: Relaxed locally correctable codes, computationally bounded channels, local expanders}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.42
Lattice-based Locality Sensitive Hashing is Optimal

Authors: Karthekeyan Chandrasekaran, Daniel Dadush, Venkata Gandikota, and Elena Grigorescu

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

Abstract
Locality sensitive hashing (LSH) was introduced by Indyk and Motwani (STOC'98) to give the first sublinear time algorithm for the c-approximate nearest neighbor (ANN) problem using only polynomial space. At a high level, an LSH family hashes "nearby" points to the same bucket and "far away" points to different buckets. The quality of measure of an LSH family is its LSH exponent, which helps determine both query time and space usage. In a seminal work, Andoni and Indyk (FOCS '06) constructed an LSH family based on random ball partitionings of space that achieves an LSH exponent of 1/c^2 for the l_2 norm, which was later shown to be optimal by Motwani, Naor and Panigrahy (SIDMA '07) and O'Donnell, Wu and Zhou (TOCT '14). Although optimal in the LSH exponent, the ball partitioning approach is computationally expensive. So, in the same work, Andoni and Indyk proposed a simpler and more practical hashing scheme based on Euclidean lattices and provided computational results using the 24-dimensional Leech lattice. However, no theoretical analysis of the scheme was given, thus leaving open the question of finding the exponent of lattice based LSH. In this work, we resolve this question by showing the existence of lattices achieving the optimal LSH exponent of 1/c^2 using techniques from the geometry of numbers. At a more conceptual level, our results show that optimal LSH space partitions can have periodic structure. Understanding the extent to which additional structure can be imposed on these partitions, e.g. to yield low space and query complexity, remains an important open problem.
Cite as

Karthekeyan Chandrasekaran, Daniel Dadush, Venkata Gandikota, and Elena Grigorescu. Lattice-based Locality Sensitive Hashing is Optimal. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chandrasekaran_et_al:LIPIcs.ITCS.2018.42,
  author =	{Chandrasekaran, Karthekeyan and Dadush, Daniel and Gandikota, Venkata and Grigorescu, Elena},
  title =	{{Lattice-based Locality Sensitive Hashing is Optimal}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{42:1--42:18},
  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.2018.42},
  URN =		{urn:nbn:de:0030-drops-83470},
  doi =		{10.4230/LIPIcs.ITCS.2018.42},
  annote =	{Keywords: Locality Sensitive Hashing, Approximate Nearest Neighbor Search, Random Lattices}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.46
Local Testing for Membership in Lattices

Authors: Karthekeyan Chandrasekaran, Mahdi Cheraghchi, Venkata Gandikota, and Elena Grigorescu

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
Testing membership in lattices is of practical relevance, with applications to integer programming, error detection in lattice-based communication and cryptography. In this work, we initiate a systematic study of local testing for membership in lattices, complementing and building upon the extensive body of work on locally testable codes. In particular, we formally define the notion of local tests for lattices and present the following: 1. We show that in order to achieve low query complexity, it is sufficient to design one-sided non-adaptive canonical tests. This result is akin to, and based on an analogous result for error-correcting codes due to Ben-Sasson et al. (SIAM J. Computing, 35(1):1-21). 2. We demonstrate upper and lower bounds on the query complexity of local testing for membership in code formula lattices. We instantiate our results for code formula lattices constructed from Reed-Muller codes to obtain nearly-matching upper and lower bounds on the query complexity of testing such lattices. 3. We contrast lattice testing from code testing by showing lower bounds on the query complexity of testing low-dimensional lattices. This illustrates large lower bounds on the query complexity of testing membership in knapsack lattices. On the other hand, we show that knapsack lattices with bounded coefficients have low-query testers if the inputs are promised to lie in the span of the lattice.
Cite as

Karthekeyan Chandrasekaran, Mahdi Cheraghchi, Venkata Gandikota, and Elena Grigorescu. Local Testing for Membership in Lattices. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chandrasekaran_et_al:LIPIcs.FSTTCS.2016.46,
  author =	{Chandrasekaran, Karthekeyan and Cheraghchi, Mahdi and Gandikota, Venkata and Grigorescu, Elena},
  title =	{{Local Testing for Membership in Lattices}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.46},
  URN =		{urn:nbn:de:0030-drops-68818},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.46},
  annote =	{Keywords: Lattices, Property Testing, Locally Testable Codes, Complexity Theory}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.151
Deciding Orthogonality in Construction-A Lattices

Authors: Karthekeyan Chandrasekaran, Venkata Gandikota, and Elena Grigorescu

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. A fundamental problem in both domains is the Closest Vector Problem (popularly known as CVP). It is well-known that CVP can be easily solved in lattices that have an orthogonal basis if the orthogonal basis is specified. This motivates the orthogonality decision problem: verify whether a given lattice has an orthogonal basis. Surprisingly, the orthogonality decision problem is not known to be either NP-complete or in P. In this paper, we focus on the orthogonality decision problem for a well-known family of lattices, namely Construction-A lattices. These are lattices of the form C + qZ^n, where C is an error-correcting q-ary code, and are studied in communication settings. We provide a complete characterization of lattices obtained from binary and ternary codes using Construction- A that have an orthogonal basis. This characterization leads to an efficient algorithm solving the orthogonality decision problem, which also finds an orthogonal basis if one exists for this family of lattices. We believe that these results could provide a better understanding of the complexity of the orthogonality decision problem in general.
Cite as

Karthekeyan Chandrasekaran, Venkata Gandikota, and Elena Grigorescu. Deciding Orthogonality in Construction-A Lattices. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 151-162, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{chandrasekaran_et_al:LIPIcs.FSTTCS.2015.151,
  author =	{Chandrasekaran, Karthekeyan and Gandikota, Venkata and Grigorescu, Elena},
  title =	{{Deciding Orthogonality in Construction-A Lattices}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{151--162},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.151},
  URN =		{urn:nbn:de:0030-drops-56509},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.151},
  annote =	{Keywords: Orthogonal Lattices, Construction-A, Orthogonal Decomposition, Lattice isomorphism}
}
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