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Gilbert, Seth (Ed.)Byzantine consensus is a classical problem in distributed computing. Each node in a synchronous system starts with a binary input. The goal is to reach agreement in the presence of Byzantine faulty nodes. We consider the setting where communication between nodes is modelled via an undirected communication graph. In the classical pointtopoint communication model all messages sent on an edge are private between the two endpoints of the edge. This allows a faulty node to equivocate, i.e., lie differently to its different neighbors. Different models have been proposed in the literature that weaken equivocation. In the local broadcast model, every message transmitted by a node is received identically and correctly by all of its neighbors. In the hypergraph model, every message transmitted by a node on a hyperedge is received identically and correctly by all nodes on the hyperedge. Tight network conditions are known for each of the three cases. We introduce a more general model that encompasses all three of these models. In the local multicast model, each node u has one or more local multicast channels. Each channel consists of multiple neighbors of u in the communication graph. When node u sends a message on a channel, itmore »

Miller, Avery (Ed.)In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network sizes that predicts the likelihood of each size occurring. The goal is to leverage the predictive power of this distribution to improve on worstcase time complexity bounds. Using a novel connection between contention resolution and information theory, we prove lower bounds on the expected time complexity with respect to the Shannon entropy of the corresponding network size random variable, for both the collision detection and no collision detection assumptions. We then analyze upper bounds for these settings, assuming now that the distribution provided as input might differ from the actual distribution generating network sizes. We express their performance with respect to both entropy and the statistical divergence between the two distributionsallowing us to quantify the cost of poor predictions. Finally, we turn our attention to the related perfect advice setting, parameterized with a length b ≥ 0, in which all active processes in a given execution are provided the best possible b bits of information about their network. We provide tight bounds on themore »

Jurdziński, T ; Schmid, S (Ed.)In the multiparty equality problem, each of the n nodes starts with a kbit input. If there is a mismatch between the inputs, then at least one node must be able to detect it. The cost of a multiparty equality protocol is the total number of bits sent in the protocol. We consider the problem of minimizing this communication cost under the local broadcast model for the case where the underlying communication graph is undirected. In the local broadcast model of communication, a message sent by a node is received identically by all of its neighbors. This is in contrast to the classical pointtopoint communication model, where a message sent by a node to one of its neighbors is received only by its intended recipient. Under pointtopoint communication, there exists a simple protocol which is competitive within a factor 2 of the lower bound [1]. In this protocol, a rooted spanning tree is fixed and each node sends its entire input to its parent in the tree. On receiving a value from its child, a node compares it against its own input to check if the two values match. Ignoring lower order additive terms, a more complicated protocol comes withinmore »

This paper considers the Byzantine consensus problem for nodes with binary inputs. The nodes are interconnected by a network represented as an undirected graph, and the system is assumed to be synchronous. Under the classical pointtopoint communication model, it is wellknown that the following two conditions are both necessary and sufficient to achieve Byzantine consensus among n nodes in the presence of up to ƒ Byzantine faulty nodes: n & 3 #8805; 3 ≥ ƒ+ 1 and vertex connectivity at least 2 ƒ + 1. In the classical pointtopoint communication model, it is possible for a faulty node to equivocate, i.e., transmit conflicting information to different neighbors. Such equivocation is possible because messages sent by a node to one of its neighbors are not overheard by other neighbors. This paper considers the local broadcast model. In contrast to the pointtopoint communication model, in the local broadcast model, messages sent by a node are received identically by all of its neighbors. Thus, under the local broadcast model, attempts by a node to send conflicting information can be detected by its neighbors. Under this model, we show that the following two conditions are both necessary and sufficient for Byzantine consensus: vertex connectivitymore »

We consider Byzantine consensus in a synchronous system where nodes are connected by a network modeled as a directed graph, i.e., communication links between neighboring nodes are not necessarily bidirectional. The directed graph model is motivated by wireless networks wherein asymmetric communication links can occur. In the classical pointtopoint communication model, a message sent on a communication link is private between the two nodes on the link. This allows a Byzantine faulty node to equivocate, i.e., send inconsistent information to its neighbors. This paper considers the local broadcast model of communication, wherein transmission by a node is received identically by all of its outgoing neighbors, effectively depriving the faulty nodes of the ability to equivocate. Prior work has obtained sufficient and necessary conditions on undirected graphs to be able to achieve Byzantine consensus under the local broadcast model. In this paper, we obtain tight conditions on directed graphs to be able to achieve Byzantine consensus with binary inputs under the local broadcast model. The results obtained in the paper provide insights into the tradeoff between directionality of communication links and the ability to achieve consensus.