Time- and Communication-Efficient Overlay Network Construction via Gossip

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph $G$ on $n$ nodes and $m$ edges, we can construct an overlay network that is a constant-degree expander in polylog $n$ rounds using only $\tilde{O}(n)$ messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only $\tilde{O}(n)$ messages, which is sublinear in $m$ (even when $m$ is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog $n$ rounds and $o(m)$ messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model.Comment: Slightly shortened abstrac

Storage and Search in Dynamic Peer-to-Peer Networks

We study robust and efficient distributed algorithms for searching, storing, and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to guarantee, despite high node churn rate, that a large number of nodes in the network can store, retrieve, and maintain a large number of data items. Our main contributions are fast randomized distributed algorithms that guarantee the above with high probability (whp) even under high adversarial churn: 1. A randomized distributed search algorithm that (whp) guarantees that searches from as many as $n - o(n)$ nodes ($n$ is the stable network size) succeed in ${O}(\log n)$-rounds despite ${O}(n/\log^{1+\delta} n)$ churn, for any small constant $\delta > 0$, per round. We assume that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time, but is oblivious to the random choices made by the algorithm). 2. A storage and maintenance algorithm that guarantees (whp) data items can be efficiently stored (with only $\Theta(\log{n})$ copies of each data item) and maintained in a dynamic P2P network with churn rate up to ${O}(n/\log^{1+\delta} n)$ per round. Our search algorithm together with our storage and maintenance algorithm guarantees that as many as $n - o(n)$ nodes can efficiently store, maintain, and search even under ${O}(n/\log^{1+\delta} n)$ churn per round. Our algorithms require only polylogarithmic in $n$ bits to be processed and sent (per round) by each node. To the best of our knowledge, our algorithms are the first-known, fully-distributed storage and search algorithms that provably work under highly dynamic settings (i.e., high churn rates per step).Comment: to appear at SPAA 201

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

Scalable Peer-to-Peer Indexing with Constant State

We present a distributed indexing scheme for peer to peer networks. Past work on distributed indexing traded off fast search times with non-constant degree topologies or network-unfriendly behavior such as flooding. In contrast, the scheme we present optimizes all three of these performance measures. That is, we provide logarithmic round searches while maintaining connections to a fixed number of peers and avoiding network flooding. In comparison to the well known scheme Chord, we provide competitive constant factors. Finally, we observe that arbitrary linear speedups are possible and discuss both a general brute force approach and specific economical optimizations