57,487 research outputs found
Computational Complexity Results for Genetic Programming and the Sorting Problem
Genetic Programming (GP) has found various applications. Understanding this
type of algorithm from a theoretical point of view is a challenging task. The
first results on the computational complexity of GP have been obtained for
problems with isolated program semantics. With this paper, we push forward the
computational complexity analysis of GP on a problem with dependent program
semantics. We study the well-known sorting problem in this context and analyze
rigorously how GP can deal with different measures of sortedness.Comment: 12 page
Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding
We consider the problem of polar coding for transmission over -user
multiple access channels. In the proposed scheme, all users encode their
messages using a polar encoder, while a multi-user successive cancellation
decoder is deployed at the receiver. The encoding is done separately across the
users and is independent of the target achievable rate. For the code
construction, the positions of information bits and frozen bits for each of the
users are decided jointly. This is done by treating the polar transformations
across all the users as a single polar transformation with a certain
\emph{polarization base}. We characterize the resolution of achievable rates on
the dominant face of the uniform rate region in terms of the number of users
and the length of the polarization base . In particular, we prove that
for any target rate on the dominant face, there exists an achievable rate, also
on the dominant face, within the distance at most
from the target rate. We then prove that the proposed MAC polar coding scheme
achieves the whole uniform rate region with fine enough resolution by changing
the decoding order in the multi-user successive cancellation decoder, as
and the code block length grow large. The encoding and decoding
complexities are and the asymptotic block error probability of
is guaranteed. Examples of achievable rates for
the -user multiple access channel are provided
Quantum Circuits for the Unitary Permutation Problem
We consider the Unitary Permutation problem which consists, given unitary
gates and a permutation of , in
applying the unitary gates in the order specified by , i.e. in
performing . This problem has been
introduced and investigated by Colnaghi et al. where two models of computations
are considered. This first is the (standard) model of query complexity: the
complexity measure is the number of calls to any of the unitary gates in
a quantum circuit which solves the problem. The second model provides quantum
switches and treats unitary transformations as inputs of second order. In that
case the complexity measure is the number of quantum switches. In their paper,
Colnaghi et al. have shown that the problem can be solved within calls in
the query model and quantum switches in the new model. We
refine these results by proving that quantum switches
are necessary and sufficient to solve this problem, whereas calls
are sufficient to solve this problem in the standard quantum circuit model. We
prove, with an additional assumption on the family of gates used in the
circuits, that queries are required, for any
. The upper and lower bounds for the standard quantum circuit
model are established by pointing out connections with the permutation as
substring problem introduced by Karp.Comment: 8 pages, 5 figure
Complexity Analysis of Balloon Drawing for Rooted Trees
In a balloon drawing of a tree, all the children under the same parent are
placed on the circumference of the circle centered at their parent, and the
radius of the circle centered at each node along any path from the root
reflects the number of descendants associated with the node. Among various
styles of tree drawings reported in the literature, the balloon drawing enjoys
a desirable feature of displaying tree structures in a rather balanced fashion.
For each internal node in a balloon drawing, the ray from the node to each of
its children divides the wedge accommodating the subtree rooted at the child
into two sub-wedges. Depending on whether the two sub-wedge angles are required
to be identical or not, a balloon drawing can further be divided into two
types: even sub-wedge and uneven sub-wedge types. In the most general case, for
any internal node in the tree there are two dimensions of freedom that affect
the quality of a balloon drawing: (1) altering the order in which the children
of the node appear in the drawing, and (2) for the subtree rooted at each child
of the node, flipping the two sub-wedges of the subtree. In this paper, we give
a comprehensive complexity analysis for optimizing balloon drawings of rooted
trees with respect to angular resolution, aspect ratio and standard deviation
of angles under various drawing cases depending on whether the tree is of even
or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns
out that some are NP-complete while others can be solved in polynomial time. We
also derive approximation algorithms for those that are intractable in general
New Bounds for the Garden-Hose Model
We show new results about the garden-hose model. Our main results include
improved lower bounds based on non-deterministic communication complexity
(leading to the previously unknown bounds for Inner Product mod 2
and Disjointness), as well as an upper bound for the
Distributed Majority function (previously conjectured to have quadratic
complexity). We show an efficient simulation of formulae made of AND, OR, XOR
gates in the garden-hose model, which implies that lower bounds on the
garden-hose complexity of the order will be
hard to obtain for explicit functions. Furthermore we study a time-bounded
variant of the model, in which even modest savings in time can lead to
exponential lower bounds on the size of garden-hose protocols.Comment: In FSTTCS 201
A GPU-accelerated Branch-and-Bound Algorithm for the Flow-Shop Scheduling Problem
Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration
methods for solving to optimality combinatorial optimization problems. In this
paper, we investigate the use of GPU computing as a major complementary way to
speed up those methods. The focus is put on the bounding mechanism of B&B
algorithms, which is the most time consuming part of their exploration process.
We propose a parallel B&B algorithm based on a GPU-accelerated bounding model.
The proposed approach concentrate on optimizing data access management to
further improve the performance of the bounding mechanism which uses large and
intermediate data sets that do not completely fit in GPU memory. Extensive
experiments of the contribution have been carried out on well known FSP
benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained
performances to a single and a multithreaded CPU-based execution. Accelerations
up to x100 are achieved for large problem instances
- âŠ