Theoretical CS Reading Group

The reading group meets once a week usually, Monday 1:30-2:30pm to discuss a particular paper or topic.

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Theory Seminar.

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Fall 2016

Wednesday, 24th August 2016 — John Kim, Swastik Kopparty
Decoding Reed-Muller codes over product sets
Presenter: GV

Friday, 9th September 2016 — Marc Bury, Chris Schwiegelshohn
Sublinear Estimation of Weighted Matchings in Dynamic Data Streams
Presenter: Samson Zhou

Wednesday, 14th September 2016 — Peter S. Landweber, Emanuel A. Lazar, and Neel Patel
On Fiber Diameters of Continuous Maps
Presenter: Abhiram Natarajan

Click to view Abstract

A surprisingly short proof that for any continuous map f : R^n -> R^m, n > m, there exists no bound on the diameter of fibers of f will be presented. Moreover, it will also be shown that when m = 1, the union of small fi bers of f is bounded; and when m > 1, the union of small fibers need not be bounded.

Friday, 23rd September 2016 — Theory Seminar - Samson Zhou, Purdue University
Nearly Optimal Sparse Group Testing

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Group testing is the process of pooling arbitrary subsets from a set of n items so as to identify, with a minimal number of disjunctive tests, a ``small'' subset of d defective items. Motivated by physical considerations, we study group testing models in which the testing procedure is constrained to be ``sparse''. Specifically, we consider (separately) scenarios in which (a) items are finitely divisible and hence may participate in at most g tests; and (b) tests are size-constrained to pool no more than r items per test. For both scenarios we provide information-theoretic lower bounds on the number of tests required to guarantee high probability recovery. Based on joint work with Venkata Gandikota, Elena Grigorescu, Sidharth Jaggi.

Monday, 26th September 2016 — Theory Seminar - Minshen Zhu, Purdue University
FPTAS for Counting Proper Four Colorings on Cubic Graphs

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Graph coloring is arguably the most exhaustively studied problem in the area of approximate counting. It is conjectured that there is a fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for counting the number of proper colorings as long as q >= D + 1, where q is the number of colors and D is the maximum degree of the graph. This bound of q = D + 1 is the uniqueness threshold. However, the conjecture remained open even for any fixed D >= 3 (The cases of D = 1, 2 are trivial). In this paper, we provide an FPTAS for counting the number of 4-colorings on graphs with maximum degree of 3 and thus confirms the conjecture in the case of D = 3. This is the first time to achieve this optimal bound of q = D + 1. Previous, the best FPRAS is for q > 11/6 D and the best deterministic FPTAS is for q > 2.581D + 1 on general graphs. For the case of D = 3, the best previous result is an FPRAS for counting 5-colorings. We note that there is a barrier to go beyond q = D + 2 for Glauber dynamics based FPRAS and we overcome this by correlation decay approach. Moreover, we develop a couple of new techniques for the correlation decay approach which can find applications in other approximate counting problems. This is joint work with Xiang Peng.

Wednesday, 28th September 2016TCS+ Talk - Swastik Kopparty, Rutgers University
High rate locally-correctable codes and locally-testable codes with subpolynomial query complexity.

Friday, 30th September 2016 — Theory Seminar - Prof. Petros Drineas, Purdue University
A Randomized Rounding Algorithm for Sparse PCA

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We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Our experimental evaluation indicates that our approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.

Wednesday, 5th October 2016 — Theory Seminar - Prof. Elena Grigorescu, Purdue University
Testing K-monotonicity

Click to view Abstract

Boolean functions are commonly used to represent a diverse set of objects: voting schemes, graphs, error-correcting codes, or concept classes.

In this talk I will introduce Boolean k-monotone functions, which are functions defined over a finite poset domain D that alternate between the values 0 and 1 at most k times on any ascending chain in D. Hence, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions.

We initiate a systematic study of k-monotone functions in the property testing model. In this model the goal is to distinguish functions that are k-monotone (or are close to being k-monotone) from functions that are far from being k-monotone. This work is motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory, and by the central role that monotonicity testing plays in the context of property testing.

I will present several results for testing k-monotonicity on the hypercube and hypergrid domains, outline some connections with distribution testing and with some learning problems, and discuss a few important open questions. Joint work with Clement Canonne, Siyao Guo, Akash Kumar, Karl Wimmer.

Wednesday, 19th October 2016 — Theory Seminar - Prof. Sam Wagstaff, Purdue University
Complexity of Factoring and Primality Testing

Wednesday, 26th October 2016TCS+ Talk - Claire Mathieu, ENS
Local search yields approximation schemes for k-means and k-median in Euclidean and minor-free metrics

Wednesday, 2nd November 2016 — Ning Chen, Arpita Ghosh, and Sergei Vassilvitskii
Optimal Envy-Free Pricing with Metric Substitutability
Presenter: Young-San Lin

Wednesday, 9th November 2016 — Peter S. Landweber, Emanuel A. Lazar, and Neel Patel
Fast and Near-Optimal Algorithms for Approximating Distributions by Histograms
Presenter: Abhiram Natarajan

Monday, 21st November 2016 — Ryan O'Donnell
SOS is not obviously automatizable, even approximately
Presenter: Akash Kumar