Tight bounds for shared memory systems accessed by Byzantine processes

We provide efficient constructions and tight bounds for shared memory systems accessed by n processes, up to t of which may exhibit Byzantine failures, in a model previously explored by Malkhi et al. [21]. We show that sticky bits are universal in the Byzantine failure model for n ≥ 3t + 1, an improvement over the previous result requiring n ≥ (2t + 1)(t + 1). Our result follows from a new strong consensus construction that uses sticky bits and tolerates t Byzantine failures among n processes for any n ≥ 3t + 1, the best possible bound on n for strong consensus. We also present tight bounds on the efficiency of implementations of strong consensus objects from sticky bits and similar primitive objects. Research supported in part by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. This work was partially completed while at AT&T Labs and while visiting the Institute for Advanced Study, Princeton, NJ. Research supported in part by US-Israel Binational Science Foundation Grant 2002246. This work was partially completed while visiting AT&T Labs. This work was partially completed while at AT&T Labs. Research supported in part by the National Science Foundation under Grant No. CCR-0331584. A preliminary version of the results presented in this paper appeared in [23].     

Representation of graphs

Summary Given a formulation of a problem, a compact representation is required both for theoretical purposes — measuring the complexity of algorithms, and for practical purposes — data compression.The adjacency lists method for representing graphs is compared to the information theoretic lower bounds, and it is shown to be optimal in many instances. For n-vertex labeled planar graphs the adjacency lists method requires 3nlogn + O(n) bits, a linear algorithm is presented to obtain a 3/2nlogn + O(n) representation while nlogn + O(n) is shown to be the minimum.     

Covering with Ellipses

We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers and present an efficient randomized approximation algorithm for the cover construction. This question is motivated by a special pattern recognition task where one has to identify ellipse-shaped protein spots in two-dimensional electrophoresis images.     

Replica compensated linear regulators for supply-regulated phase-locked loops

Supply-regulated phase-locked loops rely upon the VCO voltage regulator to maintain a low sensitivity to supply noise and hence low overall jitter. By analyzing regulator supply rejection, we show that in order to simultaneously meet the bandwidth and low dropout requirements, previous regulator implementations used in supply-regulated PLLs suffer from unfavorable tradeoffs between power supply rejection and power consumption. We therefore propose a compensation technique that places the regulator's amplifier in a local replica feedback loop, stabilizing the regulator by increasing the amplifier bandwidth while lowering its gain. Even though the forward gain of the amplifier is reduced, supply noise affects the replica output in addition to the actual output, and therefore the amplifier's gain to reject supply noise is effectively restored. Analysis shows that for reasonable mismatch between the replica and actual loads, regulator performance is uncompromised, and experimental results from a 90 nm SOI test chip confirm that with the same power consumption, the proposed regulator achieves at least 4 dB higher supply rejection than the previous regulator design. Furthermore, simulations show that if not for other supply rejection-limiting components in the PLL, the supply rejection improvement of the proposed regulator is greater than 15 dB.     

Keyword Index

Other Index

Keyword Index     

Buddy tracking — efficient proximity detection among mobile friends

Global positioning systems (GPS) and mobile phone networks make it possible to track individual users with an increasing accuracy. It is natural to ask whether this information can be used to maintain social networks. In such a network each user wishes to be informed whenever one of a list of other users, called the user’s friends, appears in the user’s vicinity. In contrast to more traditional positioning based algorithms, the computation here depends not only on the user’s own position on a static map, but also on the dynamic position of the user’s friends. Hence it requires both communication and computation resources. The computation can be carried out either between the individual users in a peer-to-peer fashion or by centralized servers where computation and data can be collected at one central location. In the peer-to-peer model, a novel algorithm for minimizing the number of location update messages between pairs of friends is presented. We also present an efficient algorithm for the centralized model, based on region hierarchy and quadtrees. The paper provides an analysis of the two algorithms, compares them with a naive approach, and evaluates them on user motions generated by the IBM City Simulator system.     

A short- time beltrami kernel for smoothing images and manifolds.

We introduce a short-time kernel for the Beltrami image enhancing flow. The flow is implemented by "convolving" the image with a space dependent kernel in a similar fashion to the solution of the heat equation by a convolution with a Gaussian kernel. The kernel is appropriate for smoothing regular (flat) 2-D images, for smoothing images painted on manifolds, and for simultaneously smoothing images and the manifolds they are painted on. The kernel combines the geometry of the image and that of the manifold into one metric tensor, thus enabling a natural unified approach for the manipulation of both. Additionally, the derivation of the kernel gives a better geometrical understanding of the Beltrami flow and shows that the bilateral filter is a Euclidean approximation of it. On a practical level, the use of the kernel allows arbitrarily large time steps as opposed to the existing explicit numerical schemes for the Beltrami flow. In addition, the kernel works with equal ease on regular 2-D images and on images painted on parametric or triangulated manifolds. We demonstrate the denoising properties of the kernel by applying it to various types of images and manifolds.