Guanfeng Liang

Iterative approximate byzantine consensus in arbitrary directed graphs

This paper proves a necessary and sufficient condition for the existence of iterative, algorithms that achieve approximate Byzantine consensus in arbitrary directed graphs, where each directed edge represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each iteration of the algorithm, the state of each fault-free node remains in the convex hull of the states of the fault-free nodes at the end of the previous iteration. The following convergence requirement is imposed: for any ε > 0, after a sufficiently large number of iterations, the states of the fault-free nodes are guaranteed to be within ε of each other. To the best of our knowledge, tight necessary and sufficient conditions for the existence of such iterative consensus algorithms in synchronous arbitrary point-to-point networks in presence of Byzantine faults, have not been developed previously. The methodology and results presented in this paper can also be extended to asynchronous systems.

When Watchdog Meets Coding

We consider the problem of misbehavior detection in wireless networks. A commonly adopted approach is to exploit the broadcast nature of the wireless medium, where nodes monitor their downstream neighbors locally using overheard messages. We call such nodes the Watchdogs. We propose a lightweight misbehavior detection scheme which integrates the idea of watchdogs and error detection coding. We show that even if the watchdog can only observe a fraction of packets, by choosing the error detection code properly, an attacker can be detected with high probability while achieving throughput arbitrarily close to optimal. Such properties reduce the incentive for the attacker to attack. We then consider the problem of locating the misbehaving node and propose a simple protocol, which locates the misbehaving node with high probability. The protocol requires exactly two watchdogs per unreliable relay node.

Error-free multi-valued consensus with byzantine failures

In this paper, we present an efficient deterministic algorithm for consensus in presence of Byzantine failures. Our algorithm achieves consensus on an L-bit value with communication complexity O(nL + n4L0.5 + n6) bits, in a network consisting of n processors with up to t Byzantine failures, such that t<<i>n/3. For large enough L, communication complexity of the proposed algorithm becomes O(nL) bits, linear in the number of processors. To achieve this goal, the algorithm performs consensus on a long message (L bits), in multiple generations, each generation performing consensus on a part of the input message. The failure-free execution of each generation is made efficient by using a combination of two techniques: error detection coding, and processor clique formation based on matching input values proposed by the processors. By keeping track of faulty behavior over the different generations, the algorithm can ensure that most generations of the algorithm are failure-free. With parameterization, our algorithm is able to achieve a large class of validity conditions for consensus, while maintaining linear communication complexity. With a suitable choice of the error detection code, and using a clique of an appropriate size, the communication cost can be traded off with the strength of the validity condition. The proposed algorithm requires no cryptographic techniques.

Experimental performance comparison of Byzantine Fault-Tolerant protocols for data centers

In this paper, we compare performance of several Byzantine agreement algorithms, including NCBA, a network coding based algorithm. Unlike existing practical BFT protocols such as PBFT by Castro and Liskov [1], which utilize collision-resistant hash functions to reduce traffic load for BFT, NCBA uses a computationally efficient error-detection network coding scheme. Since NCBA does not rely on any hash function, it is always correct rather than correct only with high probability as PBFT. Through extensive experiments, we verified that NCBA performs at least as well as Digest, without relying on any cryptographic assumption on the hardness of breaking the hash function. To the best of our knowledge, this is the first implementation of BFT with network coding.

Multiparty equality function computation in networks with point-to-point links

In this paper, we study the problem of computing the multiparty equality (MEQ) function: n ≥ 2 nodes, each of which is given an input value from {1,...,K}, determine if their inputs are all identical, under the point-to-point communication model. The MEQ function equals to 1 if and only if all n inputs are identical, and 0 otherwise. The communication complexity of the MEQ problem is defined as the minimum number of bits communicated in the worst case. It is easy to show that (n-1) log2 K bits is an upper bound, by constructing a simple algorithm with that cost. In this paper, we demonstrate that communication cost strictly lower than this upper bound can be achieved. We show this by constructing a static protocol that solves the MEQ problem for n = 3, K = 6, of which the communication cost is strictly lower than the above upper bound (2 log2 6 bits). This result is then generalized for large values of n and K.

Capacity of byzantine agreement with finite link capacity

We consider the problem of maximizing the throughput of Byzantine agreement, when communication links have finite capacity. Byzantine agreement is a classical problem in distributed computing. In existing literature, the communication links are implicitly assumed to have infinite capacity. The problem changes significantly when the capacity of links is finite. We define the throughput and capacity of agreement, and identify necessary conditions of achievable agreement throughputs. We propose an algorithm structure for achieving agreement capacity in general networks. We also introduce capacity achieving algorithms for two classes of networks: (i) arbitrary four-node networks with at most 1 failure; and (ii) symmetric networks of arbitrary size.

OCP: Opportunistic Carrier Prediction for wireless networks

In this paper, we propose Opportunistic Carrier Prediction (OCP) that jointly addresses exposed terminal and hidden terminal problems in wireless networks. OCP is based on the rationale that past interference information can be a good indicator for the outcome of future packet delivery. Each OCP sender maintains a summary of past interference information and opportunistically accesses the channel when it is confident that the packet transmission will be successful and cause no collision to other flows. To realize OCP, we propose (1) a novel data structure for each sender to summarize the interference information and (2) physical layer preemptive decoding scheme for each sender to collect the identities of the interferers. We show that OCP improves the system throughput by up to 170%, packet delivery success ratio by up to 400% in random topologies, while almost eliminating starvation.

Cooperation helps power saving

In wireless sensor networks (WSN), energy efficiency is crucial to achieving satisfactory network lifetime. The most commonly used and may be the only efficient method to reduce the energy consumption significantly is to turn off the radios most of the time, except when it has to participate in data communication. The key challenge is to operate the radio at a low duty cycle but still ensure the delay is relatively low. Various power-saving medium-access control (MAC) protocols have been proposed along this thread. However, most of such protocols focus on a point-to-point communication setting, in which a node will drop an overheard packet if it is not the destination. On the other hand, cooperative wireless communication has been drawing extensive attention in the past few years. Node cooperation has been exploited to reduce end-to-end delay, improve transmission reliability, etc. However, not much has been done in utilizing node cooperation to save energy. This idea may sound absurd since cooperation requires more nodes involved in a communication and would result in more energy being consumed. But is this true? In this paper, we will exploit the possibility of cooperative power saving in wireless ad-hoc networks. The trade-off between energy consumption and delay will be studied. Interestingly, our analytical and simulation results show that cooperation can indeed help achieve a better delay-power consumption trade-off. Our results also show that cooperation together with asymmetric power allocation can achieve the optimal delay-power trade-off.

Capacity of Byzantine consensus in capacity limited point-to-point networks

In this paper, we investigate the problem of maximizing the throughput, i.e., achieving capacity, of Byzantine consensus in point-to-point networks, in which each link has a capacity constraint. We derive an upper bound of the capacity of consensus in general point-to-point networks, and prove its tightness in 4-node complete networks by construction. We also provide a probabilistically correct algorithm that achieves the upper bound in general networks.

Capacity of byzantine agreement: summary of recent results

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, for two cases: i. communication links capacity is fixed; and ii. the sum capacity of all links in the system is fixed. Byzantine is a classical problem in distributed computing, with initial solutions presented in the seminal work of Pease, Shostak and Lamport. The notion of throughput here is similar to that used in the networking/communications literature on unicast or multicast traffic. In case i, we characterize the maximum achievable agreement throughput in four-node networks. In case ii, we identify sufficient condition for achieving agreement throughput R.