Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in d-Dimensions

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphsComment: 10 pages. 2 figures. In Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011). Replacement of version 1106.4927, reference [5] adde

A Measurement-based Analysis of the Energy Consumption of Data Center Servers

Energy consumption is a growing issue in data centers, impacting their economic viability and their public image. In this work we empirically characterize the power and energy consumed by different types of servers. In particular, in order to understand the behavior of their energy and power consumption, we perform measurements in different servers. In each of them, we exhaustively measure the power consumed by the CPU, the disk, and the network interface under different configurations, identifying the optimal operational levels. One interesting conclusion of our study is that the curve that defines the minimal CPU power as a function of the load is neither linear nor purely convex as has been previously assumed. Moreover, we find that the efficiency of the various server components can be maximized by tuning the CPU frequency and the number of active cores as a function of the system and network load, while the block size of I/O operations should be always maximized by applications. We also show how to estimate the energy consumed by an application as a function of some simple parameters, like the CPU load, and the disk and network activity. We validate the proposed approach by accurately estimating the energy of a map-reduce computation in a Hadoop platform