We present a very simple fault-tolerant atomic multicast algorithm. We suppose that we have disjoint process groups such that in each group we can realize the consensus. It is the case, for example, if, in each group, there is a majority of correct processes and if we dispose of a failure detector in 3S. This algorithm is genuine, that is, only the sender and the processes in destination groups...

In this paper we study th-order 3 consensus algorithms, which generalize the existing first-order and second-order consensus algorithms in the literature. We show necessary and sufficient conditions under which each information variable and its higherorder derivatives converge to common values. We also present the idea of higher-order consensus with a leader and introduce the concept of an th-o...

In sensor networks, sensor nodes are usually deployed randomly over an area to collect the information of interest. Data fusion is the phase of processing the collected information by sensor nodes before they are sent to the end user. This paper introduces a distributed consensus algorithm that allows the nodes of a sensor network to track the average of n sensor measurements. The study of the ...

While any fault-tolerant asynchronous consensus algorithm requires two communication steps even in failure-free executions, it is known that we can construct an algorithm terminating in one step for some good inputs (e.g. all processes propose a same value). In this paper, we present the necessary and sufficient constraint for the set of inputs for which we can construct an asynchronous consens...

This work addresses Byzantine vector consensus (BVC), wherein the input at each process is a d-dimensional vector of reals, and each process is expected to decide on a decision vector that is in the convex hull of the input vectors at the fault-free processes [3, 8]. The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space R, where d > 0 is a finite in...

This paper introduces the notion of veto number that can be associated with agreement problems. An agreement problem has veto number l when l is the minimal number of processes that control the allowed decision values, i.e., if each of them changes its mind on the value it proposes, then it forces deciding on a different value. The paper presents and investigates this concept. Key-words: Agreem...

In the exploration and implementation of formation control strategies, communication range and bandwidth limitations form a barrier to large scale formation control applications. The limitations of current formation control strategies involving a leader–follower approach and a consensus-based approach with fully available group trajectory information are explored. A unified, distributed formati...

We study the effect of communication delays on distributed consensus algorithms. Two ways to model delays on a network are presented. The first model assumes that each link delivers messages with a fixed (constant) amount of delay, and the second model is more realistic, allowing for i.i.d. time-varying bounded delays. In contrast to previous work studying the effects of delays on consensus alg...

The farthest string problem (FARTHEST STRING) is one of the core problems in the field of consensus word analysis and several biological problems such as discovering potential drugs, universal primers, or unbiased consensus sequences. Given k strings of the same length L and a nonnegative integer d, FARTHEST STRING is to find a string s such that none of the given strings has a Hamming distance...

We present a computational scheme to search for the most common motif, composed of a combination of sequence and structure constraints, among a collection of RNA sequences. The method uses a simplified version of the Sankoff algorithm for simultaneous folding and alignment of RNA sequences, but maintains tractability by constructing multi-sequence alignments from pairwise comparisons. The overa...