312,570 research outputs found
Improved Parameterized Algorithms for Constraint Satisfaction
For many constraint satisfaction problems, the algorithm which chooses a
random assignment achieves the best possible approximation ratio. For instance,
a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and
for every \eps >0 there is no polynomial-time (7/8+\eps)-approximation
unless P=NP. Another example is the {\sc Permutation CSP} of bounded arity.
Given the expected fraction of the constraints satisfied by a random
assignment (i.e. permutation), there is no (\rho+\eps)-approximation
algorithm for every \eps >0, assuming the Unique Games Conjecture (UGC).
In this work, we consider the following parameterization of constraint
satisfaction problems. Given a set of constraints of constant arity, can we
satisfy at least constraint, where is the expected fraction
of constraints satisfied by a random assignment? {\sc Constraint Satisfaction
Problems above Average} have been posed in different forms in the literature
\cite{Niedermeier2006,MahajanRamanSikdar09}. We present a faster parameterized
algorithm for deciding whether equations can be simultaneously
satisfied over . As a consequence, we obtain -variable
bikernels for {\sc boolean CSPs} of arity for every fixed , and for {\sc
permutation CSPs} of arity 3. This implies linear bikernels for many problems
under the "above average" parameterization, such as {\sc Max--Sat}, {\sc
Set-Splitting}, {\sc Betweenness} and {\sc Max Acyclic Subgraph}. As a result,
all the parameterized problems we consider in this paper admit -time
algorithms.
We also obtain non-trivial hybrid algorithms for every Max -CSP: for every
instance , we can either approximate beyond the random assignment
threshold in polynomial time, or we can find an optimal solution to in
subexponential time.Comment: A preliminary version of this paper has been accepted for IPEC 201
Systems of Linear Equations over and Problems Parameterized Above Average
In the problem Max Lin, we are given a system of linear equations
with variables over in which each equation is assigned a
positive weight and we wish to find an assignment of values to the variables
that maximizes the excess, which is the total weight of satisfied equations
minus the total weight of falsified equations. Using an algebraic approach, we
obtain a lower bound for the maximum excess.
Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin
introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75,
2009). In Max Lin AA all weights are integral and we are to decide whether the
maximum excess is at least , where is the parameter.
It is not hard to see that we may assume that no two equations in have
the same left-hand side and . Using our maximum excess results,
we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable
for a wide special case: for an arbitrary fixed function
.
Max -Lin AA is a special case of Max Lin AA, where each equation has at
most variables. In Max Exact -SAT AA we are given a multiset of
clauses on variables such that each clause has variables and asked
whether there is a truth assignment to the variables that satisfies at
least clauses. Using our maximum excess results, we
prove that for each fixed , Max -Lin AA and Max Exact -SAT AA can
be solved in time This improves
-time algorithms for the two problems obtained by Gutin et
al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively
CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks
Verifying robustness of neural network classifiers has attracted great
interests and attention due to the success of deep neural networks and their
unexpected vulnerability to adversarial perturbations. Although finding minimum
adversarial distortion of neural networks (with ReLU activations) has been
shown to be an NP-complete problem, obtaining a non-trivial lower bound of
minimum distortion as a provable robustness guarantee is possible. However,
most previous works only focused on simple fully-connected layers (multilayer
perceptrons) and were limited to ReLU activations. This motivates us to propose
a general and efficient framework, CNN-Cert, that is capable of certifying
robustness on general convolutional neural networks. Our framework is general
-- we can handle various architectures including convolutional layers,
max-pooling layers, batch normalization layer, residual blocks, as well as
general activation functions; our approach is efficient -- by exploiting the
special structure of convolutional layers, we achieve up to 17 and 11 times of
speed-up compared to the state-of-the-art certification algorithms (e.g.
Fast-Lin, CROWN) and 366 times of speed-up compared to the dual-LP approach
while our algorithm obtains similar or even better verification bounds. In
addition, CNN-Cert generalizes state-of-the-art algorithms e.g. Fast-Lin and
CROWN. We demonstrate by extensive experiments that our method outperforms
state-of-the-art lower-bound-based certification algorithms in terms of both
bound quality and speed.Comment: Accepted by AAAI 201
A Framework for Differential Frame-Based Matching Algorithms in Input-Queued Switches
This article is made available under terms and conditions applicable to Open Access Policy Articl
E-QED: Electrical Bug Localization During Post-Silicon Validation Enabled by Quick Error Detection and Formal Methods
During post-silicon validation, manufactured integrated circuits are
extensively tested in actual system environments to detect design bugs. Bug
localization involves identification of a bug trace (a sequence of inputs that
activates and detects the bug) and a hardware design block where the bug is
located. Existing bug localization practices during post-silicon validation are
mostly manual and ad hoc, and, hence, extremely expensive and time consuming.
This is particularly true for subtle electrical bugs caused by unexpected
interactions between a design and its electrical state. We present E-QED, a new
approach that automatically localizes electrical bugs during post-silicon
validation. Our results on the OpenSPARC T2, an open-source
500-million-transistor multicore chip design, demonstrate the effectiveness and
practicality of E-QED: starting with a failed post-silicon test, in a few hours
(9 hours on average) we can automatically narrow the location of the bug to
(the fan-in logic cone of) a handful of candidate flip-flops (18 flip-flops on
average for a design with ~ 1 Million flip-flops) and also obtain the
corresponding bug trace. The area impact of E-QED is ~2.5%. In contrast,
deter-mining this same information might take weeks (or even months) of mostly
manual work using traditional approaches
Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a Pure Helium Accretor
We present multidimensional simulations of the early convective phase
preceding ignition in a Type I X-ray burst using the low Mach number
hydrodynamics code, MAESTRO. A low Mach number approach is necessary in order
to perform long-time integration required to study such phenomena. Using
MAESTRO, we are able to capture the expansion of the atmosphere due to
large-scale heating while capturing local compressibility effects such as those
due to reactions and thermal diffusion. We also discuss the preparation of
one-dimensional initial models and the subsequent mapping into our
multidimensional framework. Our method of initial model generation differs from
that used in previous multidimensional studies, which evolved a system through
multiple bursts in one dimension before mapping onto a multidimensional grid.
In our multidimensional simulations, we find that the resolution necessary to
properly resolve the burning layer is an order of magnitude greater than that
used in the earlier studies mentioned above. We characterize the convective
patterns that form and discuss their resulting influence on the state of the
convective region, which is important in modeling the outburst itself.Comment: 47 pages including 18 figures; submitted to ApJ; A version with
higher resolution figures can be found at
http://astro.sunysb.edu/cmalone/research/pure_he4_xrb/ms.pd
- âŠ