4,019 research outputs found
Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks
Optimizing activation and deactivation of base station transmissions provides
an instrument for improving energy efficiency in cellular networks. In this
paper, we study optimal cell clustering and scheduling of activation duration
for each cluster, with the objective of minimizing the sum energy, subject to a
time constraint of delivering the users' traffic demand. The cells within a
cluster are simultaneously in transmission and napping modes, with cluster
activation and deactivation, respectively. Our optimization framework accounts
for the coupling relation among cells due to the mutual interference. Thus, the
users' achievable rates in a cell depend on the cluster composition. On the
theoretical side, we provide mathematical formulation and structural
characterization for the energy-efficient cell clustering and scheduling
optimization problem, and prove its NP hardness. On the algorithmic side, we
first show how column generation facilitates problem solving, and then present
our notion of local enumeration as a flexible and effective means for dealing
with the trade-off between optimality and the combinatorial nature of cluster
formation, as well as for the purpose of gauging the deviation from optimality.
Numerical results demonstrate that our solutions achieve more than 60% energy
saving over existing schemes, and that the solutions we obtain are within a few
percent of deviation from global optimum.Comment: Revision, IEEE Transactions on Wireless Communication
Fast quantum subroutines for the simplex method
We propose quantum subroutines for the simplex method that avoid classical
computation of the basis inverse. For an constraint matrix with at
most nonzero elements per column, at most nonzero elements per column
or row of the basis, basis condition number , and optimality tolerance
, we show that pricing can be performed in
time, where the
notation hides polylogarithmic factors. If the ratio is
larger than a certain threshold, the running time of the quantum subroutine can
be reduced to . The steepest edge pivoting rule also admits a quantum
implementation, increasing the running time by a factor .
Classically, pricing requires
time in the worst case using the fastest known algorithm for sparse matrix
multiplication, and with steepest
edge. Furthermore, we show that the ratio test can be performed in
time, where
determine a feasibility tolerance; classically, this requires time in
the worst case. For well-conditioned sparse problems the quantum subroutines
scale better in and , and may therefore have a worst-case asymptotic
advantage. An important feature of our paper is that this asymptotic speedup
does not depend on the data being available in some "quantum form": the input
of our quantum subroutines is the natural classical description of the problem,
and the output is the index of the variables that should leave or enter the
basis.Comment: Added discussion on condition number and infeasibilitie
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Experimental investigation of an interior search method within a simple framework
A steepest gradient method for solving Linear Programming (LP) problems, followed by a procedure for purifying a non-basic solution to an improved extreme point solution have been embedded within an otherwise simplex based optimiser. The algorithm is designed to be hybrid in nature and exploits many aspects of sparse matrix and revised simplex technology. The interior search step terminates at a boundary point which is usually non-basic. This is then followed by a series of minor pivotal steps which lead to a basic feasible solution with a superior objective function value. It is concluded that the procedures discussed in this paper are likely to have three possible applications, which are
(i) improving a non-basic feasible solution to a superior extreme point solution,
(iii) an improved starting point for the revised simplex method, and
(iii) an efficient implementation of the multiple price strategy of the revised simplex method
Efficient Methods for Automated Multi-Issue Negotiation: Negotiating over a Two-Part Tariff
In this article, we consider the novel approach of a seller and customer negotiating bilaterally about a two-part tariff, using autonomous software agents. An advantage of this approach is that win-win opportunities can be generated while keeping the problem of preference elicitation as simple as possible. We develop bargaining strategies that software agents can use to conduct the actual bilateral negotiation on behalf of their owners. We present a decomposition of bargaining strategies into concession strategies and Pareto-efficient-search methods: Concession and Pareto-search strategies focus on the conceding and win-win aspect of bargaining, respectively. An important technical contribution of this article lies in the development of two Pareto-search methods. Computer experiments show, for various concession strategies, that the respective use of these two Pareto-search methods by the two negotiators results in very efficient bargaining outcomes while negotiators concede the amount specified by their concession strategy
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