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 even under high adversarial churn. In particular, we present the following main results:1. A randomized distributed search algorithm that with high probability 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+δ n) churn, for any small constant δ > 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 and has unlimited computational power, but is oblivious to the random choices made by the algorithm).2. A storage and maintenance algorithm that guarantees, with high probability, data items can be efficiently stored (with only Θ(log n) copies of each data item) and maintained in a dynamic P2P network with churn rate up to O(n/ log 1+δ 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+δ 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). Furthermore, they are localized (i.e., do not require any global topological knowledge) and scalable. A technical contribution of this paper, which may be of independent interest, is
We consider the problem of scheduling a set of jobs on a single machine subject to inventory constraints, i.e., conditions that jobs add or remove items to or from a centralized inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We focus on scheduling problems on a single machine where the objective is to minimize the total weighted completion time. In this paper, we design 2-approximation algorithms for special cases of the problem that run in polynomial time.
Abstract. Basic graph structures such as maximal independent sets (MIS's) have spurred much theoretical research in randomized and distributed algorithms, and have several applications in networking and distributed computing as well. However, the extant (distributed) algorithms for these problems do not necessarily guarantee fault-tolerance or load-balance properties. We propose and study "low-average degree" or "balanced" versions of such structures. Interestingly, in sharp contrast to, say, MIS's, it can be shown that checking whether a structure is balanced, will take substantial time. Nevertheless, we are able to develop good sequential/distributed (randomized) algorithms for such balanced versions. We also complement our algorithms with several lower bounds. Randomization plays a key role in our upper and lower bound results.
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