Elena Grigorescu
My research interests lie broadly in theoretical computer science, with a particular emphasis on sublinear algorithms, complexity theory, coding theory and
learning theory.
My recent work has focused on the following goals:
- designing algorithms that only use sublinear time or sublinear space, in computational models relevant to large data sets
- understanding the complexity of fundamental problems on error-correcting codes and point lattices, with applications to communications,
cryptography and optimizations
- understanding information-theoretical limits of computation in diverse models.
Local links: Theory seminar,
Theory reading group,
Theory group,
Midwest Theory Day.
PC member: CSR17, RANDOM16, STOC15, CCC14, SODA14
- CS580 Algorithm Design and Analysis Fall 2017, Fall 2016, Fall 2015, Fall 2013.
- CS584 Theory of Computation/Computational Complexity, Spring 2017, Spring 2014, Spring 2013
- CS483 Intro to the Theory of Computation, Spring 2016.
- CS590 Sublinear Algorithms Spring 2015
- CS381 Intro to the Analysis of Algorithms Fall 2014
- CS590 Current Topics in Theoretical Computer Science, Fall 2012
- Discrete Fourier Analysis and Applications , Spring 2012, Georgia Tech;
Current:
Akash Kumar (PhD, co-advised with Saugata Basu)
Young-San Lin (PhD, co-advised with Thanh Nguyen)
Abhiram Natarajan (PhD, co-advised with Saugata Basu)
Samson Zhou (PhD, co-advised with Greg Frederickson)
Minshen Zhu (Masters)
Clayton Thomas (Undergraduate)
Former:
- Lattice-Based Locality Sensitive Hashing is Optimal
Karthik Chandrasekaran, Daniel Dadush, Venkata Gandikota, Elena Grigorescu
Submitted.
- Communication-Efficient Distributed Learning of Discrete Distributions
Ilias Diakonikolas, Elena Grigorescu, Jerry Li, Abhiram Natarajan, Krzysztof Onak, Ludwig Schmidt
Proceedings of NIPS 2017 (to appear). Oral presentation.
- Nearly-Optimal l2 Heavy Hitters in the Sliding Window Model
Vladimir Braverman, Elena Grigorescu, Harry Lang, Samson Zhou.
Submitted.
- Maximally Recoverable Codes: the Bounded Case
Venkata Gandikota, Elena Grigorescu, Clayton Thomas, Minshen Zhu
Proceedings of Allerton Conference on Communication, Control, and Computing, 2017. (to appear) [pdf]
- Streaming Periodicity with Mismatches
Funda Ergun, Elena Grigorescu, Erfan Sadeqi Azer, Samson Zhou.
Proceedings of RANDOM 2017 (to appear) [pdf]
- Flipping out with Many Flips: Hardness of Testing k-Monotonicity
Elena Grigorescu, Akash Kumar, Karl Wimmer.
[pdf]
(Subsumes [pdf]). Submitted.
- Streaming for Aibohphobes: Longest Palindrome with Mismatches
Elena Grigorescu, Erfan Sadeqi Azer, Samson Zhou. [pdf]
Proceedings of FSTTCS, 2017 (to appear).
- Longest Alignment with Edits in Data Streams
Elena Grigorescu, Erfan Sadeqi Azer, Samson Zhou. [pdf]
Proceedings of Allerton Conference on Communication, Control, and Computing, 2017 (to appear)
- Structural Results on Matching Estimation with Applications to Streaming
Marc Bury, Elena Grigorescu, Andrew McGregor, Morteza Monemizadeh, Chris Schwiegelshohn, Sofya Vorotnikova, Samson Zhou [pdf]
(Joint journal version of this, this, and this.)
Submitted.
- Testing k-Monotonicity (The Rise and Fall of Boolean Functions)
Clément Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer.
Accepted to Theory of Computing, 2017. Preliminary version in the Proceedings of Innovations in Theoretical Computer Science (ITCS), 2017.
[pdf]
- Streaming Weighted Matchings: Optimal Meets Greedy
Elena Grigorescu, Morteza Monemizadeh, Samson Zhou.
Submitted.
[pdf].
- Local Testing of Lattices
Karthik Chandrasekaran, Mahdi Cheraghchi, Venkata Gandikota, Elena Grigorescu.
Proceedings of FSTTCS 2016.
[conference]
[full]
- Nearly Optimal Sparse Group Testing
Venkata Gandikota, Elena Grigorescu, Sidharth Jaggi, Samson Zhou.
Proceedings of Allerton Conference on Communication, Control, and Computing, 2016.
[conference]
[full]
- NP-hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem
Venkata Gandikota, Badih Ghazi, Elena Grigorescu.
Proceedings of FOCS 2016.
[conference]
[full]
- AC0-MOD2 Lower Bounds for the Boolean Inner-Product
Mahdi Cheraghchi, Elena Grigorescu, Brendan Juba, Karl Wimmer, Ning Xie.
Proceedings of ICALP 2016.
[conference]
[full]
We show super-linear bounds for the problem of computing the Inner-Product function on AC0 circuits with parity gates just above the input level.
- Deciding Orthogonality in Construction-A Lattices
Karthik Chandrasekaran, Venkata Gandikota, Elena Grigorescu
SIDMA, 2017. Preliminary version in Foundations of Software Technology and Theoretical Computer Science (FSTTCS) 2015.
[pdf]
We show that the problem of deciding if a lattice has an orthogonal basis can be solved efficiently in Construction-A lattices.
- On the NP-hardness of Bounded Distance Decoding of Reed-Solomon Codes
Venkata Gandikota, Badih Ghazi, Elena Grigorescu
IEEE International Symposium on Information Theory (ISIT) 2015.
[conference]
[full]
We show that it is NP-hard to decode RS codes if the amount of error is very close to the covering radius of the code.
- Tight Lower Bounds for Testing Linear Isomorphism
Elena Grigorescu, Karl Wimmer, Ning Xie.
Proceedings of RANDOM 2013.
[pdf]
We show a tight adaptive, two-sided lower bound for testing linear isomorphism to the inner-product function.
This is the first lower bound for testing linear isomorphism to a specific function that matches the trivial upper bound.
We also show an exponential query lower bound for any adaptive, two-sided tester for membership in a large subclass of bent functions.
- A Lower-Variance Randomized Algorithm for Approximate String Matching
Mikhail Atallah, Elena Grigorescu,Yi Wu.
Information Processing Letters, 2013.
[pdf]
We provide an unbiased estimator for the score of matches between a text string and a pattern string, of smaller variance than in previous algorithms.
- Statistical Algorithms and a Lower Bound for Planted Clique
Vitaly Feldman, Elena Grigorescu, Lev Reyzin, Santosh Vempala, Ying Xiao.
J. ACM 2017. Preliminary version in Proceedings of STOC 2013.
[conference]
[full]
We introduce a framework for proving lower bounds on computational problems over distributions, based on defining a restricted class of algorithms called statistical algorithms.
For well-known problems over distributions, we give lower bounds on the complexity of any statistical algorithm.
These include a nearly optimal lower bound for detecting planted bipartite clique distributions (or planted dense subgraph distributions) when the planted clique has small size.
- List Decoding Barnes-Wall Lattices
Elena Grigorescu, Chris Peikert.
Computational Complexity, 2017. Preliminary version in Proceedings of the Conference on Computational Complexity (CCC), 2012
[pdf]
Motivated by the similar discrete linear structure of linear codes and point lattices, and their many shared applications, we initiate the study of list decoding for lattices. We focus on combinatorial and algorithmic questions related to list decoding for the well-studied family of Barnes-Wall lattices.
Our results imply a polynomial-time list-decoding algorithm for any error radius bounded away from the minimum distance, thus beating a typical barrier for natural error-correcting codes posed by the Johnson radius.
- Testing Odd-Cycle Freeness in Boolean Functions
Arnab Bhattacharyya, Elena Grigorescu, Prasad Raghavendra, Asaf Shapira.
Combinatorics, Probability and Computing 21(6): 835-855, 2012. Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), 2012.
[conference]
[full]
We continue the study of boolean linear-invariant properties defined over the hypercube and draw more connections to the testability of dense graphs.
We show that an important family in this class (called `odd-cycle free') is efficiently testable.
We also show that a canonical tester for this property only blows up the query complexity polynomially.
These results suggest new open questions that attempt to cast light into the larger program of characterizing testable linear-invariant properties.
- Explicit Low-Weight Bases for BCH Codes
Elena Grigorescu, Tali Kaufman.
IEEE Transactions on Information Theory, 2011.
[pdf]
Motivated by applications in property testing, we investigate explicit low-weight codewords and bases of low-weight codewords for the well-studied BCH codes.
We exhibit such codewords in some restricted settings.
- On Noise Tolerant Learning of Sparse Parities and Related Problems
Elena Grigorescu, Lev Reyzin, Santosh Vempala.
Proceedings of the International Conference
on
Algorithmic Learning Theory (ALT), 2011. [pdf]
We propose an improved algorithm for learning sparse parities over arbitrary distributions.
- On Sums of Locally Testable Affine Invariant Properties
Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, Madhu Sudan.
Proceedings of the International Workshop on Randomization and Computation (RANDOM), 2011.
[conference]
[full]
Linear codes (properties) that are also affine-invariant represent well-studied objects in the areas of local-testing, local-correcting, and local-decoding.
An important open question in algebraic property testing is: what are neccessary and sufficient conditions that unify the testability of all these properties?
The notion of `single-orbit' has been identified in the literature as a promising structural feature that leads to testability.
This notion allows us in this work to broaden the class of known testable affine invariant properties by considering a basic, yet nontrivial operation on properties that have a single orbit, namely summation. Our results here together with previous results from the literature suggest the first conjecture that attempts to essentially capture the structure of all testable affine invariant properties.
- Steiner Transitive-Closure Spanners of Low-Dimensional Posets
Peter Berman, Arnab Bhattacharyya, Elena Grigorescu, Sofya Raskhodnikova, David Woodruff, Grigory Yaroslavtsev.
Combinatorica 34(3): 255-277 (2014). Preliminary version in
Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP), 2011.
[conference]
[full]
Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners for partially ordered sets.
We present a nearly tight lower bound on the size of Steiner 2-TC-spanners of d-dimensional directed hypergrids. It implies better lower bounds on the complexity of local reconstructors of monotone functions and functions with low Lipschitz constant.
We also show a lower bound on the size of Steiner k-TC-spanners of d-dimensional posets that almost matches the known upper bounds.
- Separations of Matroid Freeness Properties
Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordström, Ning Xie.
Technical Report TR10-136, Electronic Colloquium on Computational Complexity (ECCC), August 2010. [pdf]
We focus again on boolean linear-invariant properties over the hypercube defined by forbidden patterns.
We initiate a systematic study of these properties from the somewhat subtle point of view that different local characterizations by forbidden patterns
can lead to properties that are essentially the same in a property testing sense. We identify a combinatorial tool (called `labelled matroid homomorphism')
that captures the relationship between the constraints in a way relevant to the question of distinguishing the respective properties that they define.
- Symmetries in Algebraic Property Testing Elena Grigorescu
PhD Thesis, MIT, 2010.
- A Unified Framework for Testing Linear-Invariant Properties
Arnab Bhattacharyya, Elena Grigorescu, Asaf Shapira .
Random Struct. Algorithms 46(2): 232-260 (2015). Preliminary version in
Proceedings of the Symposium on Foundations of Computer Science (FOCS), 2010.
[conference]
[full]
We propose a framework for analyzing the testability of boolean linear-invariant properties defined over the hypercube by drawing ideas from
mysterious syntactic connections to the testability of graph properties, which is an area well-understood.
Our results show the testability of a large class of linear-invariant properties, defined by forbidding a possibly infinite collection of arbitrary patterns.
Based on these results we formulate the first conjecture that attempts to unify the testability of all boolean properties that are invariant under linear transformations
and are testable with one sided error.
- Lower Bounds for Local Monotonicity Reconstructors from Transitive-Closure Spanners
Arnab Bhattacharyya, Elena Grigorescu, Madhav Jha, Kyomin Jung, Sofya Raskhodnikova, David Woodruff.
SIAM Journal on Discrete Mathematics 26(2): 618-646 (2012). Proceedings of the International Workshop on Randomization and Computation (RANDOM), 2010.
[conference]
[full]
We continue the study of Transitive Closure Spanners and reveal a connection to `local monotonicity reconstructors', which are algorithms that reconstruct monotone functions from corrupted versions, in a distributed manner.
This connection allows us to derive lower bounds on the query complexity of local monotonicity reconstructors from lower bounds on the size of TC-spanners.
We study such lower bounds on directed hypercubes and hypergrids.
- A Local Decision Test for Sparse Polynomials
Elena Grigorescu, Kyomin Jung, Ronitt Rubinfeld .
Information Processing Letters, v.110, n.20, 898-901, 2010. [pdf]
We show a local test for deciding if a polynomial is sparse or not.
- Error-Correcting Data Structures
Victor Chen,
Elena Grigorescu,
Ronald de Wolf.
SIAM Journal on Computing 42(1): 84-111 (2013). Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 2010.
[conference]
[full]
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability.
In this work, we study two data structure problems: membership and polynomial evaluation. We show that these two problems have constructions that are simultaneously efficient and error-correcting.
- Succinct Representation of Codes with Applications to Testing
Elena Grigorescu, Tali Kaufman, Madhu Sudan.
SIAM Journal on Discrete Mathematics 26(4): 1618-1634 (2012). Proceedings of the International Workshop on Randomization and Computation (RANDOM), 2009.
[conference]
[full]
We show that the dual of every ``sparse'' binary code whose symmetry group includes the group of non-singular affine transformations, has the single local orbit property (i.e., it is specified by a single local constraint and its translations under the affine group. )
This class includes the dual-BCH codes for whose duals (i.e., for BCH codes) simple bases were not known.
- Transitive-Closure Spanners
Arnab Bhattacharyya ,
Elena Grigorescu,
Kyomin Jung,
Sofya Raskhodnikova,
David Woodruff.
SIAM Journal on Computing 41(6): 1380-1425 (2012). Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 2009.
[conference]
[full]
We introduce the notion of Transitive-Closure spanners of a directed graph as a common abstraction to applications in data structures, monotonicity testing and access control. We present algorithms for approximating the size of the sparsest k-TC spanner, and prove strong hardness results for this problem. In addition, our structural bounds for path-separable (directed) graphs lead to improved monotonicity testers for these posets.
- 2-Transitivity is Insufficient for Local Testability
Elena Grigorescu, Tali Kaufman, Madhu Sudan.
Journal of Computational Complexity 22(1): 137-158 (2013).
Proceedings of the Conference on Computational Complexity (CCC), 2008.
[conference]
[full]
In this work we refute a conjecture from the literature, stating that the presence of a single low weight codeword in the dual of a code, and ``2-transitivity'' of the code (i.e., the code is invariant under a 2-transitive group of permutations on the coordinates of the code) suffice to imply local testability.
- Decodability of Group Homomorphisms Beyound the Johnson Bound
Irit Dinur, Elena Grigorescu, Swastik Kopparty, Madhu Sudan.
Proceedings of the ACM Symposium on Theory of Computing (STOC), 2008.
[conference]
[full]
We show that the code whose codewords are the homomorphisms between any two finite abelian groups is locally list decodable from a fraction of errors arbitrarily close to its minimum distance. The heart of the argument is a combinatorial result which gives an upper bound on the number of codewords in within a certain distance from any given word.
- Local Decoding and Testing for Homomorphisms
Elena Grigorescu, Swastik Kopparty, Madhu Sudan.
Proceedings of the International Workshop on Randomization and Computation (RANDOM), 2006.
[conference]
[full]
We initiate a systematic study of local decoding of codes based on group homomorphisms. We present an efficient local list decoder for codes from any abelian group G to a fixed abelian group H. Our results give a new generalization of the classical work of Goldreich and Levin, and give a new abstraction of the list decoder of Sudan, Trevisan and Vadhan.
- The Insulation Sequence of a Graph
Elena Grigorescu
Discrete Applied Mathematics, Volume 134, Issues 1-3, 2004, 77-90. [pdf]
We consider certain generalizations of independent sets, called insulated sets, and completely characterize the possible orderings of an insulated sequence of a graph.
- Decreasing the Diameter of Cycles
Elena Grigorescu
Journal of Graph Theory, Volume 43, Issues 4, 2003, 299-303. [pdf]
We improve some lower bounds on the number of edges to be added to a cycle in order to decrease its diameter to 2 or 3.
* The copyright for these documents belongs to the respective publishers.
E-mail: elena-g (at) purdue (dot) edu
Office: 765 496 1185
1209 Lawson Computer Science Building,
305 N. University Ave.
West Lafayette, IN 47907