An Algorithm to Calculate Optimal Homogeneous Systems of Parameters

AbstractWhen a homogeneous system of parametersf1,...,fnis chosen for a graded algebraA, it is important for subsequent computations that the degrees, deg(fi), are as small as possible. More precisely, one would like the product or the sum of the degrees to be minimal, depending on the application.This article investigates which degree vectors can occur as the degrees of a homogeneous system of parameters. From this, an algorithm is derived which constructs an optimal homogeneous system of parameters. Here the notion of what is considered asoptimalis part of the input. An important application is the case whereAis the invariant ring of a finite linear group. There is an implementation of the algorithm in Magma which applies to this case

Movement-Efficient Sensor Deployment in Wireless Sensor Networks With Limited Communication Range.

We study a mobile wireless sensor network (MWSN) consisting of multiple mobile sensors or robots. Three key factors in MWSNs, sensing quality, energy consumption, and connectivity, have attracted plenty of attention, but the interaction of these factors is not well studied. To take all the three factors into consideration, we model the sensor deployment problem as a constrained source coding problem. %, which can be applied to different coverage tasks, such as area coverage, target coverage, and barrier coverage. Our goal is to find an optimal sensor deployment (or relocation) to optimize the sensing quality with a limited communication range and a specific network lifetime constraint. We derive necessary conditions for the optimal sensor deployment in both homogeneous and heterogeneous MWSNs. According to our derivation, some sensors are idle in the optimal deployment of heterogeneous MWSNs. Using these necessary conditions, we design both centralized and distributed algorithms to provide a flexible and explicit trade-off between sensing uncertainty and network lifetime. The proposed algorithms are successfully extended to more applications, such as area coverage and target coverage, via properly selected density functions. Simulation results show that our algorithms outperform the existing relocation algorithms

DyMo: Dynamic Monitoring of Large Scale LTE-Multicast Systems

LTE evolved Multimedia Broadcast/Multicast Service (eMBMS) is an attractive solution for video delivery to very large groups in crowded venues. However, deployment and management of eMBMS systems is challenging, due to the lack of realtime feedback from the User Equipment (UEs). Therefore, we present the Dynamic Monitoring (DyMo) system for low-overhead feedback collection. DyMo leverages eMBMS for broadcasting Stochastic Group Instructions to all UEs. These instructions indicate the reporting rates as a function of the observed Quality of Service (QoS). This simple feedback mechanism collects very limited QoS reports from the UEs. The reports are used for network optimization, thereby ensuring high QoS to the UEs. We present the design aspects of DyMo and evaluate its performance analytically and via extensive simulations. Specifically, we show that DyMo infers the optimal eMBMS settings with extremely low overhead, while meeting strict QoS requirements under different UE mobility patterns and presence of network component failures. For instance, DyMo can detect the eMBMS Signal-to-Noise Ratio (SNR) experienced by the 0.1% percentile of the UEs with Root Mean Square Error (RMSE) of 0.05% with only 5 to 10 reports per second regardless of the number of UEs