We establish an O(n log² n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of n log n). The fastest previously known algorithm for this problem works in time O(n 3=2 ). Using our broadcasting algorithm, we develop an O(n 3=2 log 2 n) algorithm for gossiping in the same network model.

Defect tolerance will become more important as feature sizes shrink closer to single digit nanometer dimensions. This is true whether the chips are manufactured using topdown methods (e.g., photolithography) or bottom-up methods (e.g., chemically assembled electronic nanotechnology, or CAEN). In this paper, we propose a defect tolerance methodology centered around reconfigurable devices, a scalable testing method, and dynamic place-and-route. Our methodology is particularly well suited for CAEN.

... In this paper, we focus on another collection of recent applications in the general area of communications, including cryptography and networking. Applications have been chosen to represent those in which design theory plays a useful, and sometimes central, role. Moreover, applications have been chosen to reflect in addition the genesis of new and interesting problems in design theory in order to treat the practical concerns. Of many candidates, thirteen applications areas have been included. They are as follows:

Recently, Ethernet celebrated its twentieth anniversary. Over those years, the processing speed of the attached hosts has increased by several orders of magnitude, to the point where the relative bandwidth of a 10 Mbps Ethernet has fallen from more than adequate to support large enterprise networks (whose utilizations were typically only a few percent, anyway), to marginally fast enough to support a single high performance desktop workstation. At the same time, the Ethernet standard has also evolved to incorporate new technology at the physical layer, including new media, new signalling methods, and support for higher data rates. However, the MAC layer protocols have remained essentially unchanged from the early days of undemanding applications running on large numbers of slow hosts. In this paper, we argue that it is time to review the MAC layer and incorporate advances made in the protocol performance field over the last twenty years. First, we describe several little-known facts abo...

As the dominating CMOS technology is fast approaching a “brick wall,” new opportunities arise for competing solutions. Nanoelectronics has achieved several breakthroughs lately and promises to overcome many of the limitations intrinsic to current semiconductor approaches. Most of the results in this area reported until now focus on devices and interconnect; this work goes several steps further and presents issues related to circuits and architecture. Based on proposed nanoscale interconnect and device structures, we explore the design space available to the nanoelectronic circuit designer and system architect.

Multiple Access protocols are distributed algorithms that enable a set of geographically dispersed stations to communicate using a single, common, broadcast channel. We concentrate on the class of Conflict Resolution Algorithms. This class exhibits very good performance characteristics for ‘‘bursty’ ’ computer communications traffic, including high capacity, low delay under light traffic conditions, and inherent stability. One algorithm in this class achieves the highest capacity among all known multiple-access protocols for the infinite population Poisson model. Indeed, this capacity is not far from a theoretical upper bound. After surveying the most important and influential Conflict Resolution Algorithms, the emphasis in our presentation is shifted to methods for their analysis and results of their performance evaluation. We also discuss some extensions of the basic protocols and performance results for non-standard environments, such as Local Area Networks, satellite channels, channels with errors, etc., providing a comprehensive bibliography. 1. Conflict Resolution Based Random Access Protocols The ALOHA protocols were a breakthrough in the area of multiple access communications. 1 They delivered, more or less, what they advertized, i.e., low delay for bursty, computer generated traffic. They suffer, however, from stability problems and low capacity. 2 The next major breakthrough in the area of multiple access communications

Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive pooling (or group testing) problem involves identifying the bad objects using the least number of tests applied in parallel. The `hypergeometric ' case occurs when an upper bound on the number of bad objects is known a priori. Here, practical considerations lead us to impose the additional requirement of a posteriori confirmation that the bound is satisfied. A generalization of the problem in which occasional errors in the test outcomes can occur is also considered. Optimal solutions to the general problem are shown to be equivalent to maximum-size collections of subsets of a finite set satisfying a union condition which generalizes that considered by Erdos et al. [3]. Lower bounds on the number of tests required are derived when the number of bad objects is believed to be either 1 or 2. Steiner systems are shown to be optimal solutions in some cases.

Ding-Zhu Du We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be ¡-error-detecting ¢¤£¥§ ¦ and thus ¡-error-correcting, where, a positive integer, is the maximum number of defectives (or positives). Hence, the number of errors which can be detected grows linearly with the number of positives. Also, this construction induces a construction of a binary code with minimum Hamming distance ¨ ¨ at least. The second design � is the-analogue of a known construction on ¡-disjunct matrices. 1

In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. This approach gives a unified probabilistic treatment of these questions. It simplifies and extends some of the results known in this domain. 1. Introduction. A

Group testing is a long studied problem in combinatorics: A small set of r ill people should be identified out of the whole (n people) by using only queries (tests) of the form “Does set X contain an ill human?”. In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This scheme has Θ � min[r 2 log n, n] � tests which is as many as the best non-explicit schemes have. In our construction we use a fact that may have a value by its own right: Linear error-correction codes with parameters [m, k, δm]q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in Θ � q k m � time.