1,624 research outputs found
Special Section on the Forty-First Annual ACM Symposium on Theory of Computing (STOC 2009)
This issue of SICOMP contains nine specially selected papers from the Forty-first Annual ACM Symposium on the Theory of Computing, otherwise known as STOC 2009, held May 31 to June 2 in Bethesda, Maryland. The papers here were chosen to represent both the excellence and the broad range of the STOC program. The papers have been revised and extended by the authors, and subjected to the standard thorough reviewing process of SICOMP.
The program committee consisted of Susanne Albers, Andris Ambainis, Nikhil Bansal, Paul Beame, Andrej Bogdanov, Ran Canetti, David Eppstein, Dmitry Gavinsky, Shafi Goldwasser, Nicole Immorlica, Anna Karlin, Jonathan Katz, Jonathan Kelner, Subhash Khot, Ravi Kumar, Leslie Ann Goldberg, Michael Mitzenmacher (Chair), Kamesh Munagala, Rasmus Pagh, Anup Rao, Rocco Servedio, Mikkel Thorup, Chris Umans, and Lisa Zhang. They accepted 77 papers out of 321 submissions
A Hypergraph Dictatorship Test with Perfect Completeness
A hypergraph dictatorship test is first introduced by Samorodnitsky and
Trevisan and serves as a key component in their unique games based \PCP
construction. Such a test has oracle access to a collection of functions and
determines whether all the functions are the same dictatorship, or all their
low degree influences are Their test makes queries and has
amortized query complexity but has an inherent loss of
perfect completeness. In this paper we give an adaptive hypergraph dictatorship
test that achieves both perfect completeness and amortized query complexity
.Comment: Some minor correction
Distributed PCP Theorems for Hardness of Approximation in P
We present a new distributed model of probabilistically checkable proofs
(PCP). A satisfying assignment to a CNF formula is
shared between two parties, where Alice knows , Bob knows
, and both parties know . The goal is to have
Alice and Bob jointly write a PCP that satisfies , while
exchanging little or no information. Unfortunately, this model as-is does not
allow for nontrivial query complexity. Instead, we focus on a non-deterministic
variant, where the players are helped by Merlin, a third party who knows all of
.
Using our framework, we obtain, for the first time, PCP-like reductions from
the Strong Exponential Time Hypothesis (SETH) to approximation problems in P.
In particular, under SETH we show that there are no truly-subquadratic
approximation algorithms for Bichromatic Maximum Inner Product over
{0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate
Regular Expression Matching, and Diameter in Product Metric. All our
inapproximability factors are nearly-tight. In particular, for the first two
problems we obtain nearly-polynomial factors of ; only
-factor lower bounds (under SETH) were known before
Tight Lower Bounds for Differentially Private Selection
A pervasive task in the differential privacy literature is to select the
items of "highest quality" out of a set of items, where the quality of each
item depends on a sensitive dataset that must be protected. Variants of this
task arise naturally in fundamental problems like feature selection and
hypothesis testing, and also as subroutines for many sophisticated
differentially private algorithms.
The standard approaches to these tasks---repeated use of the exponential
mechanism or the sparse vector technique---approximately solve this problem
given a dataset of samples. We provide a tight lower
bound for some very simple variants of the private selection problem. Our lower
bound shows that a sample of size is required
even to achieve a very minimal accuracy guarantee.
Our results are based on an extension of the fingerprinting method to sparse
selection problems. Previously, the fingerprinting method has been used to
provide tight lower bounds for answering an entire set of queries, but
often only some much smaller set of queries are relevant. Our extension
allows us to prove lower bounds that depend on both the number of relevant
queries and the total number of queries
Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations
We study approximation algorithms for scheduling problems with the objective
of minimizing total weighted completion time, under identical and related
machine models with job precedence constraints. We give algorithms that improve
upon many previous 15 to 20-year-old state-of-art results. A major theme in
these results is the use of time-indexed linear programming relaxations. These
are natural relaxations for their respective problems, but surprisingly are not
studied in the literature.
We also consider the scheduling problem of minimizing total weighted
completion time on unrelated machines. The recent breakthrough result of
[Bansal-Srinivasan-Svensson, STOC 2016] gave a -approximation for the
problem, based on some lift-and-project SDP relaxation. Our main result is that
a -approximation can also be achieved using a natural and
considerably simpler time-indexed LP relaxation for the problem. We hope this
relaxation can provide new insights into the problem
Testing Linear-Invariant Non-Linear Properties
We consider the task of testing properties of Boolean functions that are
invariant under linear transformations of the Boolean cube. Previous work in
property testing, including the linearity test and the test for Reed-Muller
codes, has mostly focused on such tasks for linear properties. The one
exception is a test due to Green for "triangle freeness": a function
f:\cube^{n}\to\cube satisfies this property if do not all
equal 1, for any pair x,y\in\cube^{n}.
Here we extend this test to a more systematic study of testing for
linear-invariant non-linear properties. We consider properties that are
described by a single forbidden pattern (and its linear transformations), i.e.,
a property is given by points v_{1},...,v_{k}\in\cube^{k} and
f:\cube^{n}\to\cube satisfies the property that if for all linear maps
L:\cube^{k}\to\cube^{n} it is the case that do
not all equal 1. We show that this property is testable if the underlying
matroid specified by is a graphic matroid. This extends
Green's result to an infinite class of new properties.
Our techniques extend those of Green and in particular we establish a link
between the notion of "1-complexity linear systems" of Green and Tao, and
graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the
proceedings of STACS 200
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