Most cellular network communication strategies are focused on data traffic scenarios rather than energy balance and efficient utilization. Thus mobile users(cell phones) in hot cells may suffer from low throughput due to energy loading imbalance problem. In state-of-art cellular network technologies, relay stations extend cell coverage and enhance signal strength for mobile users. However, busy traffic makes the relay stations in hot area run out of energy quickly. In this paper, we propose an energy balancing strategy in which the mobile nodes are able to dynamically select and hand over to the relay station with the highest potential energy capacity to resume communication. Key to the strategy is that each relay station merely maintains two parameters that contains the trend of its previous energy consumption and then predicts its future quantity of energy, which is defined as the relay station's potential energy capacity. Then each mobile node can select the relay station with the highest potential energy capacity. Simulations demonstrate that our approach significantly increase the aggregate throughput and the average life time of relay stations in cellular network environment.

We explore the problem of computing a nearest singular matrix to a given regular Hankel matrix while preserving the structure of the matrix. Nearness is measured in a matrix norm, or a componentwise norm. A recent result for structured condition numbers leads to an efficient algorithm in the spectral norm. We devise a parametrization of singular Hankel matrices, to discuss other norms.

this paper is very special: nearness is measured coefficient-wise, i.e., in infinity norm. And the root locus is parametric, namely, the real axis. All previous solutions seem to have required that for parametric root locations the distance expression is at least differentiable: they and we have proven results using the Euclidean distance. Infinity norm leads us [7] to linear programming problems, whose parametric versions we do not know how to solve efficiently. We can solve our specific problem efficiently, that is in polynomial-time in the degree and input length, because an explicit expression for the distance to the nearest polynomial with a real root can be derived from a result in [17], or alternatively by eigenvalue analysis of companion matrices in [15, Section 4.2]. The expression involves absolute values, but by a stroke of luck can be minimized over the entire real axis.

Continuous changes of the coecients of a polynomial move the roots continuously.We consider the problem nding the minimal perturbations to the coecients to move a root to a given locus, such as a single point, the real or imaginary axis, the unit circle, or the right half plane.We measure minimality in both the Euclidean distance to the coecient vector and maximal coecient-wise change in absolute value (in nity norm), either with entirely real or with complex coecients.If the locus is a piecewise parametric curve, we can give ecient, i.e., polynomial time algorithms for the Euclidean norm; for the in nity norm we present an ecient algorithm when a root of the minimally perturbed polynomial is constrained to a single point.In terms of robust control, we are able to compute the radius of stability i n t h e Euclidean norm for a wide range of convex open domains of the complex plane.

This contribution to the ongoing discussion of division algorithm for residue number systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a high level of modularity, and makes the complexity analysis more transparent. The number of iterations needed is logarithmic in the size of the quotient for a fixed start value. With preconditioning it becomes the logarithm of the input bit size. An implementation of the conversion to mixed radix representation is outlined in the appendix.>