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

Fast Distributed PageRank Computation

Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search engine). In distributed computing alone, PageRank vector, or more generally random walk based quantities have been used for several different applications ranging from determining important nodes, load balancing, search, and identifying connectivity structures. Surprisingly, however, there has been little work towards designing provably efficient fully-distributed algorithms for computing PageRank. The difficulty is that traditional matrix-vector multiplication style iterative methods may not always adapt well to the distributed setting owing to communication bandwidth restrictions and convergence rates. In this paper, we present fast random walk-based distributed algorithms for computing PageRanks in general graphs and prove strong bounds on the round complexity. We first present a distributed algorithm that takes O\big(\log n/\eps \big) rounds with high probability on any graph (directed or undirected), where $n$ is the network size and \eps is the reset probability used in the PageRank computation (typically \eps is a fixed constant). We then present a faster algorithm that takes O\big(\sqrt{\log n}/\eps \big) rounds in undirected graphs. Both of the above algorithms are scalable, as each node sends only small (\polylog n) number of bits over each edge per round. To the best of our knowledge, these are the first fully distributed algorithms for computing PageRank vector with provably efficient running time.Comment: 14 page