Enabling Robust and Efficient Distributed Computation in Dynamic Peer-to-Peer Networks

Motivated by the need for designing efficient and robust fully-distributed computation in highly dynamic networks such as Peer-to-Peer (P2P) networks, we study distributed protocols for constructing and maintaining dynamic network topologies with good expansion properties. Our goal is to maintain a sparse (bounded degree) expander topology despite heavy {\em churn} (i.e., nodes joining and leaving the network continuously over time). We assume that the churn is controlled by an adversary that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is a randomized distributed protocol that guarantees with high probability the maintenance of a {\em constant} degree graph with {\em high expansion} even under {\em continuous high adversarial} churn. Our protocol can tolerate a churn rate of up to $O(n/\poly\log(n))$ per round (where $n$ is the stable network size). Our protocol is efficient, lightweight, and scalable, and it incurs only $O(\poly\log(n))$ overhead for topology maintenance: only polylogarithmic (in $n$) bits needs to be processed and sent by each node per round and any node's computation cost per round is also polylogarithmic. The given protocol is a fundamental ingredient that is needed for the design of efficient fully-distributed algorithms for solving fundamental distributed computing problems such as agreement, leader election, search, and storage in highly dynamic P2P networks and enables fast and scalable algorithms for these problems that can tolerate a large amount of churn.

Fast Byzantine Leader Election in Dynamic Networks

We study the fundamental Byzantine leader election problem in dynamic networks where the topology can change from round to round and nodes can also experience heavy {\em churn} (i.e., nodes can join and leave the network continuously over time). We assume the full information model where the Byzantine nodes have complete knowledge about the entire state of the network at every round (including random choices made by all the nodes), have unbounded computational power and can deviate arbitrarily from the protocol. The churn is controlled by an adversary that has complete knowledge and control over which nodes join and leave and at what times and also may rewire the topology in every round and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is an $O(\log^3 n)$ round algorithm that achieves Byzantine leader election under the presence of up to $O({n}^{1/2 - \epsilon})$ Byzantine nodes (for a small constant $\epsilon > 0$) and a churn of up to \\$O(\sqrt{n}/\poly\log(n))$ nodes per round (where $n$ is the stable network size).The algorithm elects a leader with probability at least $1-n^{-\Omega(1)}$ and guarantees that it is an honest node with probability at least $1-n^{-\Omega(1)}$; assuming the algorithm succeeds, the leader's identity will be known to a $1-o(1)$ fraction of the honest nodes. Our algorithm is fully-distributed, lightweight, and is simple to implement. It is also scalable, as it runs in polylogarithmic (in $n$) time and requires nodes to send and receive messages of only polylogarithmic size per round.To the best of our knowledge, our algorithm is the first scalable solution for Byzantine leader election in a dynamic network with a high rate of churn; our protocol can also be used to solve Byzantine agreement in a straightforward way.We also show how to implement an (almost-everywhere) public coin with constant bias in a dynamic network with Byzantine nodes and provide a mechanism for enabling honest nodes to store information reliably in the network, which might be of independent interest.