55,790 research outputs found
Solving the subset-sum problem with a light-based device
We propose a special computational device which uses light rays for solving
the subset-sum problem. The device has a graph-like representation and the
light is traversing it by following the routes given by the connections between
nodes. The nodes are connected by arcs in a special way which lets us to
generate all possible subsets of the given set. To each arc we assign either a
number from the given set or a predefined constant. When the light is passing
through an arc it is delayed by the amount of time indicated by the number
placed in that arc. At the destination node we will check if there is a ray
whose total delay is equal to the target value of the subset sum problem (plus
some constants).Comment: 14 pages, 6 figures, Natural Computing, 200
An optical solution for the set splitting problem
We describe here an optical device, based on time-delays, for solving the set
splitting problem which is well-known NP-complete problem. The device has a
graph-like structure and the light is traversing it from a start node to a
destination node. All possible (potential) paths in the graph are generated and
at the destination we will check which one satisfies completely the problem's
constrains.Comment: 10 pages, 2 figure
Exact Cover with light
We suggest a new optical solution for solving the YES/NO version of the Exact
Cover problem by using the massive parallelism of light. The idea is to build
an optical device which can generate all possible solutions of the problem and
then to pick the correct one. In our case the device has a graph-like
representation and the light is traversing it by following the routes given by
the connections between nodes. The nodes are connected by arcs in a special way
which lets us to generate all possible covers (exact or not) of the given set.
For selecting the correct solution we assign to each item, from the set to be
covered, a special integer number. These numbers will actually represent delays
induced to light when it passes through arcs. The solution is represented as a
subray arriving at a certain moment in the destination node. This will tell us
if an exact cover does exist or not.Comment: 20 pages, 4 figures, New Generation Computing, accepted, 200
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
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