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

Where Graph Topology Matters: The Robust Subgraph Problem

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall vulnerability to external attacks or random failures. In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)? We define a robust subgraph as a subset of nodes with high communicability among them, and formulate the RLS-PROBLEM of finding a subgraph of given size with maximum robustness in the host graph. Our formulation is related to the recently proposed general framework for the densest subgraph problem, however differs from it substantially in that besides the number of edges in the subgraph, robustness also concerns with the placement of edges, i.e., the subgraph topology. We show that the RLS-PROBLEM is NP-hard and propose two heuristic algorithms based on top-down and bottom-up search strategies. Further, we present modifications of our algorithms to handle three practical variants of the RLS-PROBLEM. Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs even at lower densities, suggesting that the existing approaches are not suitable for the new problem setting.Comment: 13 pages, 10 Figures, 3 Tables, to appear at SDM 2015 (9 pages only