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Towards robust and efficient computation in dynamic peer-to-peer networks. SODA '12 Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms, 551-569.

We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The two-state case, in which there is a single active and a single sleep state, is a continuous version of the ski-rental problem. We consider a generalized version in which there is more than one sleep state, each with its own power-consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of 3 + 2 √ 2 ≈ 5.828 for any system.

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We introduce a communication model for hybrid networks, where nodes have access to two different communication modes: a local mode where (like in traditional networks) communication is only possible between specific pairs of nodes, and a global mode where (like in overlay networks) communication between any pair of nodes is possible. This can be motivated, for instance, by wireless networks in which we combine direct device-to-device communication (e.g., using WiFi) with communication via a shared infrastructure (like base stations, the cellular network, or satellites).Typically, communication over short-range connections is cheaper and can be done at a much higher rate. Hence, we are focusing here on the LOCAL model (in which the nodes can exchange an unbounded amount of information in each round) for the local connections while for the global communication we assume the so-called node-capacitated clique model, where in each round every node can exchange only O(log n)-bit messages with just O(log n) other nodes. However, our model for hybrid networks is very general so that it can also capture many other scenarios, like the congested clique model.In order to explore the power of combining local and global communication, we study the complexity of computing shortest paths in the graph given by the local connections. We show that our model allows the development of algorithms that are significantly faster than what can be done by using either local or global communication only.We specifically show the following results. For the all-pairs shortest paths problem (APSP), we show that an exact solution can be computed in timeÕ n 2/3 1 and that approximate solutions can be computed in timeΘ √ n . For the single-source shortest paths problem (SSSP), we show that an exact solution can be computed in timeÕ √ SPD , where SPD denotes the shortest path diameter. We further show that a 1+o(1) -approximate solution can be computed in timeÕ n 1/3 . Additionally, we show that for every constant ε > 0, it is possible to compute an O(1)-approximate solution in timeÕ(n ε ).1 Note that theÕ(·)-notation hides factors that are polylogarithmic in n.Many existing communication networks exploit a combination of multiple communication modes to maximize cost-efficiency and throughput. As a prominent example, hybrid datacenter networks combine highspeed optical or wireless circuit switching technologies with traditional electronic packet switches to offer higher throughput at lower cost [14,21]. In the Internet, dynamic multipoint VPNs can be set up to connect different branches of an organization by combining leased lines (offering them quality-of-service guarantees for their mission-critical traffic) with standard, best-effort VPN connections (for their lower-priority traffic) [35]. Alternatively, an organization may also set up a so-called hybrid WAN by combining their own communication infrastructure with connections via the Internet [38]. Finally, the emerging 5G standard promises to allow smartphones to not only communicate via the ce...

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

Abstract. An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team's profit is given by a convex function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.