199,729 research outputs found
The computational complexity of the Chow form
We present a bounded probability algorithm for the computation of the Chow
forms of the equidimensional components of an algebraic variety. Its complexity
is polynomial in the length and in the geometric degree of the input equation
system defining the variety. In particular, it provides an alternative
algorithm for the equidimensional decomposition of a variety.
As an application we obtain an algorithm for the computation of a subclass of
sparse resultants, whose complexity is polynomial in the dimension and the
volume of the input set of exponents. As a further application, we derive an
algorithm for the computation of the (unique) solution of a generic
over-determined equation system.Comment: 60 pages, Latex2
ThumbNet: One Thumbnail Image Contains All You Need for Recognition
Although deep convolutional neural networks (CNNs) have achieved great
success in computer vision tasks, its real-world application is still impeded
by its voracious demand of computational resources. Current works mostly seek
to compress the network by reducing its parameters or parameter-incurred
computation, neglecting the influence of the input image on the system
complexity. Based on the fact that input images of a CNN contain substantial
redundancy, in this paper, we propose a unified framework, dubbed as ThumbNet,
to simultaneously accelerate and compress CNN models by enabling them to infer
on one thumbnail image. We provide three effective strategies to train
ThumbNet. In doing so, ThumbNet learns an inference network that performs
equally well on small images as the original-input network on large images.
With ThumbNet, not only do we obtain the thumbnail-input inference network that
can drastically reduce computation and memory requirements, but also we obtain
an image downscaler that can generate thumbnail images for generic
classification tasks. Extensive experiments show the effectiveness of ThumbNet,
and demonstrate that the thumbnail-input inference network learned by ThumbNet
can adequately retain the accuracy of the original-input network even when the
input images are downscaled 16 times
On Optimality of Myopic Policy for Restless Multi-armed Bandit Problem with Non i.i.d. Arms and Imperfect Detection
We consider the channel access problem in a multi-channel opportunistic
communication system with imperfect channel sensing, where the state of each
channel evolves as a non independent and identically distributed Markov
process. This problem can be cast into a restless multi-armed bandit (RMAB)
problem that is intractable for its exponential computation complexity. A
natural alternative is to consider the easily implementable myopic policy that
maximizes the immediate reward but ignores the impact of the current strategy
on the future reward. In particular, we develop three axioms characterizing a
family of generic and practically important functions termed as -regular
functions which includes a wide spectrum of utility functions in engineering.
By pursuing a mathematical analysis based on the axioms, we establish a set of
closed-form structural conditions for the optimality of myopic policy.Comment: Second version, 16 page
Fast recursive grayscale morphology operators: from the algorithm to the pipeline architecture
International audienceThis paper presents a new algorithm for an efficient computation of morphological operations for gray images and its specific hardware. The method is based on a new recursive morphological decomposition method of 8-convex structuring elements by only causal two-pixel structuring elements (2PSE). Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan involving a fixed reduced analysis neighborhood. The resulting process offers low computation complexity combined with easy description of the element form. The dedicated hardware is generic and fully regular, built from elementary interconnected stages. It has been synthesized into an FPGA and achieves high frequency performances for any shape and size of structuring element
The degree of the central curve in semidefinite, linear, and quadratic programming
The Zariski closure of the central path which interior point algorithms track
in convex optimization problems such as linear, quadratic, and semidefinite
programs is an algebraic curve. The degree of this curve has been studied in
relation to the complexity of these interior point algorithms, and for linear
programs it was computed by De Loera, Sturmfels, and Vinzant in 2012. We show
that the degree of the central curve for generic semidefinite programs is equal
to the maximum likelihood degree of linear concentration models. New results
from the intersection theory of the space of complete quadrics imply that this
is a polynomial in the size of semidefinite matrices with degree equal to the
number of constraints. Besides its degree we explore the arithmetic genus of
the same curve. We also compute the degree of the central curve for generic
linear programs with different techniques which extend to the computation of
the same degree for generic quadratic programs.Comment: 15 page
Secure Computation with Sublinear Amortized Work
Traditional approaches to secure computation begin by representing
the function being computed as a circuit. For any function~ that depends on each of its inputs, this implies a protocol with complexity at least linear in the input size. In fact, linear running time is inherent for secure computation of non-trivial functions, since each party must ``touch\u27\u27 every bit of their input lest information about other party\u27s input be leaked. This seems to rule out many interesting applications of secure computation in scenarios where at least one of the inputs is huge and sublinear-time algorithms can be utilized in the insecure setting; private database search is a prime example.
We present an approach to secure two-party computation that yields sublinear-time protocols, in an amortized sense, for functions that can be computed in sublinear time on a random access machine~(RAM). Furthermore, a party whose input is ``small\u27\u27 is required to maintain
only small state. We provide a generic protocol that achieves the claimed complexity, based on any oblivious RAM and any protocol for
secure two-party computation. We then present an optimized version of this protocol, where generic secure two-party computation is used only for evaluating a small number of simple operations
A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems
We improve the local generic position method for isolating the real roots of
a zero-dimensional bivariate polynomial system with two polynomials and extend
the method to general zero-dimensional polynomial systems. The method mainly
involves resultant computation and real root isolation of univariate polynomial
equations. The roots of the system have a linear univariate representation. The
complexity of the method is for the bivariate case, where
, resp., is an upper bound on the degree, resp., the
maximal coefficient bitsize of the input polynomials. The algorithm is
certified with probability 1 in the multivariate case. The implementation shows
that the method is efficient, especially for bivariate polynomial systems.Comment: 24 pages, 5 figure
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