Showing papers by "Andrei Z. Broder published in 1984"

Flipping Coins In Many Pockets (Byzantine Agreement On Uniformly Random Values)

Abstract: It was recently shown by Michael Rabin that a sequence of random 0-1 values, prepared and distributed by a trusted "dealer," can be used to achieve Byzantine agreement in constant expected time in a network of processors. A natural question is whether it is possible to generate these values uniformly at random within the network. In this paper we present a cryptography based protocol for agreernent on a 0-1 randona value, if less than half of the processors are faulty. In fact the protocol allows uniform sampling from any finite set, and thus solves the problem of choosing a network leader uniformly at random. The protocol is usable both when all the communication is via "broadcast," in which case it needs three rounds of information exchange, and when each pair of processors communicate on a private line, in which case it needs 3t + 3 rounds, where t is the number of faulty proccssors. The protocol remains valid even if passive eavesdropping is allowed. On the other hand we show that no (probabilistic) protocol can achieve agreement on a fair coin in fewer phases then necessary for Byzantine agreement, and hence the "pre-dealt" nature of the random sequence required for Rabin's algorithm is crucial.

Efficient fault tolerant routings in networks

Abstract: We analyze the problem of constructing a network which will have a fixed routing and which will be highly fault tolerant. A construction is presented which forms a “product route graph” from two or more constituent “route graphs.” The analysis involves the surviving route graph, which consists of all non-faulty nodes in the network with two nodes being connected by a directed edge iff the route from the first to the second is still intact after a set of component failures. The diameter of the surviving route graph, that is, the maximum distance between any pair of nodes, is a measure of the worst-case performance degradation caused by the faults. The number of faults tolerated, the diameter, and the degree of the product graph are related in a simple way to the corresponding parameters of the constituent graphs. In addition, there is a “padding theorem” which allows one to add nodes to a graph and to extend a previous routing.

Pessimal algorithms and simplexity analysis

Abstract: The twin disciplines of Pessimal Algorithm Design and Simplexity Analysis are introduced and illustrated by means of representative problems