20,619 research outputs found
Semidefinite programming and eigenvalue bounds for the graph partition problem
The graph partition problem is the problem of partitioning the vertex set of
a graph into a fixed number of sets of given sizes such that the sum of weights
of edges joining different sets is optimized. In this paper we simplify a known
matrix-lifting semidefinite programming relaxation of the graph partition
problem for several classes of graphs and also show how to aggregate additional
triangle and independent set constraints for graphs with symmetry. We present
an eigenvalue bound for the graph partition problem of a strongly regular
graph, extending a similar result for the equipartition problem. We also derive
a linear programming bound of the graph partition problem for certain Johnson
and Kneser graphs. Using what we call the Laplacian algebra of a graph, we
derive an eigenvalue bound for the graph partition problem that is the first
known closed form bound that is applicable to any graph, thereby extending a
well-known result in spectral graph theory. Finally, we strengthen a known
semidefinite programming relaxation of a specific quadratic assignment problem
and the above-mentioned matrix-lifting semidefinite programming relaxation by
adding two constraints that correspond to assigning two vertices of the graph
to different parts of the partition. This strengthening performs well on highly
symmetric graphs when other relaxations provide weak or trivial bounds
A Partial Taxonomy of Substitutability and Interchangeability
Substitutability, interchangeability and related concepts in Constraint
Programming were introduced approximately twenty years ago and have given rise
to considerable subsequent research. We survey this work, classify, and relate
the different concepts, and indicate directions for future work, in particular
with respect to making connections with research into symmetry breaking. This
paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint
Satisfaction Problems (SymCon'10
FEâBE Coupling Methods for Elastoplasticity
Non-linear physical systems of infinite extent are conveniently modelled using FEâBE coupling methods. By the combination of both methods, suitable use of the advantages of each one may be obtained. Several possibilities of FEMâBEM coupling and their performance in some practical cases are discussed in this paper. Parallelizable coupling algorithms based on domain decomposition are developed and compared with the most traditional coupling methods
Symmetric complex-valued RBF receiver for multiple-antenna aided wireless systems
A nonlinear beamforming assisted detector is proposed for multiple-antenna-aided wireless systems employing complex-valued quadrature phase shift-keying modulation. By exploiting the inherent symmetry of the optimal Bayesian detection solution, a novel complex-valued symmetric radial basis function (SRBF)-network-based detector is developed, which is capable of approaching the optimal Bayesian performance using channel-impaired training data. In the uplink case, adaptive nonlinear beamforming can be efficiently implemented by estimating the systemâs channel matrix based on the least squares channel estimate. Adaptive implementation of nonlinear beamforming in the downlink case by contrast is much more challenging, and we adopt a cluster-variationenhanced clustering algorithm to directly identify the SRBF center vectors required for realizing the optimal Bayesian detector. A simulation example is included to demonstrate the achievable performance improvement by the proposed adaptive nonlinear beamforming solution over the theoretical linear minimum bit error rate beamforming benchmark
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