Adapting the interior point method for the solution of linear programs on high performance computers

In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes better use of high performance computer architecture than the sparse simplex method. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is beneficial

Energy-efficient power allocation for point-to-point MIMO systems over the rayleigh fading channel

It is well-established that transmitting at full power is the most spectral-efficient power allocation strategy for point-to-point (P2P) multi-input multi-output (MIMO) systems, however, can this strategy be energy efficient as well? In this letter, we address the most energy-efficient power allocation policy for symmetric P2P MIMO systems by accurately approximating in closed-form their optimal transmit power when a realistic MIMO power consumption model is considered. In most cases, being energy efficient implies a reduction in transmit and overall consumed powers at the expense of a lower spectral efficiency

Minimum power multicasting with delay bound constraints in Ad Hoc wireless networks

In this paper, we design a new heuristic for an important extension of the minimum power multicasting problem in ad hoc wireless networks. Assuming that each transmission takes a fixed amount of time, we impose constraints on the number of hops allowed to reach the destination nodes in the multicasting application. This setting would be applicable in time critical or real time applications, and the relative importance of the nodes may be indicated by these delay bounds. We design a filtered beam search procedure for solving this problem. The performance of our algorithm is demonstrated on numerous test cases by benchmarking it against an optimal algorithm in small problem instances, and against a modified version of the well-known Broadcast Incremental Power (BIP) algorithm 20 for relatively large problems