Rutgers/DIMACS
Theory of Computing Seminar
Fall 2014
Place: CoRE 301 (NOTE THE ROOM FOR THIS
SEMESTER)
Time: Wednesdays 11:00 am 
12:00 Noon
Organizers: Swastik Kopparty and Shubhangi
Saraf
Directions
For those arriving by train to New Brunswick station, the best way
to get to the seminar room is by Rutgers bus. The directions are available by
clicking here.
For those driving in, the best strategy is to prearrange to pick up a parking
tag from one of the organizers upon arrival, and park in lot 64. For directions
to Lot 64, click on this link.
Links
·
The Rutgers discrete
math seminar.
·
Other Math and CS seminars at
Rutgers.
·
Theory of Computing seminars from previous
semesters.
Schedule
September 10 
Anand Sarwate Rutgers 
Active Learning with Asymmetric
Costs In some learning problems, unlabeled data is
freely available, but labeling is costly since it must be done by an expert.
Active learning approaches have been shown in many cases to be quite
effective in reducing the labeling cost. Active learning algorithms
sequentially select points to be labeled to more efficiently explore the
hypothesis space. In some applications the cost of labeling may depend on the
label value; a positive label may result in a reward, for example. We study
an extreme version of this problem, which we call auditing: for binary
labels, querying a point with positive label costs nothing, while a negative
label costs a single point. In this talk I will describe this new problem,
how the new cost structure leads to different algorithms and asymptotic costs
than regular active learning for specific hypothesis classes, as well as a
competitive approach for the general case. I will close with some ongoing
work on applying active learning to problems in linear classification and
subspace learning. Much of this work is with Sivan Sabato (Ben Gurion U.) and Nati Srebro (TTIChicago/Technion) 
September 17 
Omri Weinstein Princeton University 
Approximating the best Nash
Equilibrium in n^{o(log n)}time breaks the Exponential Time Hypothesis The celebrated PPAD hardness result for finding an
exact Nash equilibrium in a twoplayer game initiated a quest for finding
*approximate* Nash equilibria efficiently, and is one of the major open
questions in algorithmic game theory. We study the computational complexity of finding an \epsapproximate Nash equilibrium with good social
welfare. Hazan and Krauthgamer
and subsequent improvements showed that finding an epsilonapproximate Nash
equilibrium with good social welfare in a two player game and many variants
of this problem is at least as hard as finding a planted clique of size O(log
n) in the random graph G(n,1/2). We show that any polynomial time algorithm that
finds an \epsapproximate Nash equilibrium with good
social welfare refutes (the worstcase) Exponential Time Hypothesis by Impagliazzo and Paturi.
Specifically, it would imply a 2^O(\sqrt{n}) algorithm for SAT. Our lower bound matches the quasipolynomial time
algorithm by Lipton, Markakis and Mehta for solving
the problem. Our key tool is a reduction from the PCP machinery to finding
Nash equilibrium via free games, the framework introduced in the recent work
by Aaronson, Impagliazzo and Moshkovitz.
Techniques developed in the process may be useful for replacing planted
clique hardness with ETHhardness in other applications. Joint work with Mark Braverman
and Young Kun Ko. 
September 24 

NO
SEMINAR (mass
absences) 
October 1 
Sanjeev Arora Princeton University 
Adventures in Linear Algebra++
and unsupervised learning Many problems in unsupervised learning are
NPcomplete. To design efficient algorithms with provable guarantees, one
must move away from worstcase complexity and make specific assumptions about
the input instances. The talk will survey some successes we and others have
had in designing such provable algorithms for nononegative
matrix factorization, topic modeling, deep learning, hidden markov models, etc. The techniques used in these can be
seen as new variants of classical linear algebra: what we think of as Linear
Algebra++. 
October 8 
Amir Shpilka Technion 
ReedMuller codes with respect
to random errors and erasures In TCS we usually study error correcting codes
with respect to the Hamming metric, i.e. we study their behaviour
with respect to worst case errors. However, in coding theory a more common model
is that of random errors, where Shannon’s results show a much better
tradeoff between rate and decoding radius. We consider the behaviour
of ReedMuller codes in the Shannon model of random errors. In particular, we
show that RM codes with either low or highdegree (n^1/2 or nn^1/2,
respectively), with high probability, can decode from an 1r fraction of random erasures (where r
is the rate). In other words, for this range of parameters RM codes achieve
capacity for the BinaryErasureChannel. This result matches experimental
observations that RM codes can achieve capacity for the BEC, similarly to
Polar codes. We also show that RMcodes can handle many more random errors
than the minimum distance, i.e. roughly n^d/2
errors for codes of degree nd (where the minimum distance is only 2^d). We show that the questions regarding the behaviour of ReedMuller codes wrt
random errors are tightly connected to the following question. Given a random
set of vectors in {0,1}^n, what is the probability
the their d’th tensor products are linearly
independent? We obtain our results by giving answer to this question for
certain range of parameters. Based
on a joint work with Emmanuel Abbe and Avi Wigderson. 
October
15 
Gil Cohen Weizmann Institute 
BiLipschitz
Bijection between the Boolean Cube and the Hamming
Ball We construct a biLipschitz
bijection from the Boolean cube to the Hamming ball
of equal volume. More precisely, we show that for all even n, there exists an
explicit bijection f from the ndimensional Boolean
cube to the Hamming ball of equal volume embedded in (n+1)dimensional
Boolean cube, such that for all x and y it holds that dist(x,y) / 5 <= dist(f(x),f(y)) <= 4 dist(x,y), where dist(,) denotes the
Hamming distance. This result gives a strong negative answer to an
open problem of Lovett and Viola [CC 2012], who raised the question in the
context of sampling distributions in lowlevel complexity classes. The
conceptual implication is that the problem of proving lower bounds in the context
of sampling distributions requires ideas beyond the sensitivitybased
structural results of Boppana [IPL 97]. No prior knowledge is assumed. Joint work with Itai Benjamini and Igor Shinkar. 
October 22 
Bhaskar DasGupta UIC 
Complexity of Measuring Global
Stability of Banking Networks Threats on the stability of a financial system may
severely affect the functioning of the entire economy, and thus considerable
emphasis is placed on the analyzing the cause and effect of such threats. The
financial crisis in the current and past decade has shown that one important
cause of instability in global markets is the socalled financial contagion,
namely the socalled financial contagion process in which failures of few
individual banks propagate through the "web of banking
dependencies" to affect a significant part of the entire financial
system. Motivated by such observations, we consider the problem of defining
and evaluating stabilities of both homogeneous and heterogeneous banking networks
against propagation of synchronous idiosyncratic shocks given to a subset of
banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version,
formalize the synchronous shock propagation procedures, define two
appropriate stability measures and investigate the computational complexities
of evaluating these measures for various network topologies and parameters of
interest. Time permitting, we will also discuss
empirical evaluation of our global stability measure for several classes of
banking networks, and some interesting implications of our evaluations. 
October 29 
Jop Briët NYU 
Locally decodable codes and Banachspace geometry (Based on joint work with Assaf
Naor and Oded Regev) Locally decodable codes (LDCs) are error
correcting codes that allow any symbol of an encoded message to be retrieved
by querying only a small number of randomly selected codeword
symbols, even if the codeword is partially
corrupted. A main open problem is to determine what the smallestpossible codeword length of such codes is when the query
complexity is a fixed constant. This talk is about a link between this
problem and basic properties of certain Banach
spaces that has implications in two directions. In one direction the link
gives a short alternative proof of the known exponential lower bound on the
length of binary 2query LDCs due to Kerenidis and
de Wolf ('04). In the other direction it shows that the known existence of
subexponentiallength 3query LDCs implies the answer to an open question
about the geometry of tensor products of l_p
spaces. 
November
5 
Alan Selman University of Buffalo 
Disjoint NPpairs and
Propositional Proof Systems This talk surveys results on disjoint NPpairs, propositional
proof systems, function classes, and promise classes  including results that
demonstrate close connections that bind these topics together. We illustrate important links between the
questions of whether these classes have complete objects and whether optimal
proof systems may exist. 
November 12 
Noga RonZewi IAS 
Limitations of Public Key
Encryption from Noisy Codewords Several wellstudied public key encryption
schemes, including those of Alekhnovich (FOCS
2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan
(STOC 2008), rely on the conjectured intractability of inverting a noisy
linear encoding. These schemes are limited in that they either require the
underlying field to grow polynomially with the
security parameter, or alternatively they can work over the binary field but
have a low noise entropy that gives rise to
subexponential attacks. Motivated by the goal of achieving efficient public
key cryptography, we study the possibility of obtaining improved security
over the binary field by using different noise distributions. For this, we first propose a unified framework
that captures all three encryption schemes mentioned above and allows for arbitrary
choices of the underlying field and noise distributions. We then show, using a simple argument that relies
on agnostic learning of parities (Kalai, Mansour
and Verbin, STOC 2008), that any instance of the
unified framework over the binary field can be attacked in time exp(n/log(n))
where n is the ciphertext size. Combining this
attack with Regev's security proof (STOC 2005) we
obtain an algorithm that solves the learning parity with noise (LPN) problem
in time exp(n/loglog(n))
using only n^{1+\epsilon} samples, reproducing the result of Lyubashevsky
(Random 2005) and Kopparty and Saraf
(STOC 2010) in a conceptually different way. Our main result shows a new connection between
additive combinatorics and public key encryption by showing that the
``approximate duality conjecture" from additive combinatorics (BenSasson and R., STOC 2011) improves the running time of
the above attack to exp(sqrt(n)) where n is the maximum
of the ciphertext size and the public key size. On
the positive side, counter examples to the above conjecture may lead to
candidate distributions over the binary field with improved security
guarantees. Joint work with Eli BenSasson,
Iddo BenTov, Ivan Damgard
and Yuval Ishai. 
November 19 
Eric Allender Rutgers 
Zero Knowledge and Circuit
Minimization For roughly four decades, two of the beststudied
problems in NP that are not known to be in P or to be NP complete have been: * Graph Isomorphism, and * MCSP (the Minimum Circuit Size Problem). Yet there had been no theorem, relating the
complexity of these two problems to each other. Until now. We give a simple argument  drawing on the
connection between MCSP and timebounded Kolmogorov complexity  showing that not only Graph
Isomorphism, but every problem in the complexity class SZK (Statistical Zero Knowledge) is BPP reducible to
MCSP. Joint work with Bireswar
Das. 
November 26 

NO
SEMINAR (the
day before Thanksgiving) 
December 3 
Noga Alon IAS/Tel Aviv University 
Sign Rank, Spectral Gap and VC dimension The signrank of an N by
N matrix A of signs is the minimum possible rank of a real matrix B in which
every entry has the same sign as the corresponding entry of A. The
VCdimension of A is the maximum cardinality of a set of columns I of A so that
for every subset J of I there is a row i of A so
that A_{ij}=+1 for all j in J and A_{ij}=1
for all j in IJ. I will describe explicit examples of N by N
matrices with VCdimension 2 and signrank Omega(N^{1/4}). I will also discuss the maximum possible signrank of an N by N matrix with VCdimension d. We
conjecture that this maximum is N^{11/d}, up to
logarithmic factors, and can prove that this is the case for d \leq 2. I will also mention briefly the applications of
these results to communication complexity and learning. Joint work with Shay Moran and Amir Yehudayoff. 
December 10 
Michael Kapralov IBM Watson 
Approximating matching size
from random streams We present a streaming algorithm that makes one
pass over the edges of an unweighted graph
presented in {\em random} order, and produces a polylogarithmic approximation to the size of the maximum
matching in the graph, while using only polylogarithmic
space. Prior to this work the only approximations known were a folklore $\tilde{O}(\sqrt{n})$
approximation with polylogarithmic space in an $n$
vertex graph and a constant approximation with $\Omega(n)$ space. Our work
thus gives the first algorithm where both the space and approximation factors
are smaller than any polynomial in $n$. Our algorithm is obtained by effecting a streaming
implementation of a simple ``local'' algorithm that we design for this problem.
The local algorithm produces a $O(k\cdot n^{1/k})$ approximation to the size of a maximum
matching by exploring the radius $k$ neighborhoods of vertices, for any
parameter $k$. We show, somewhat surprisingly, that our local algorithm can
be implemented in the streaming setting even for $k = \Omega(\log
n/\log\log n)$. Our analysis exposes some of the problems that arise in such
conversions of local algorithms into streaming ones, and gives techniques to
overcome such problems. This is joint work with Sanjeev Khanna and Madhu Sudan 