The Forgiving Graph: a distributed data structure for low stretch under adversarial attack

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick “repairs,” which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes v and w whose distance would have been l in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most l log n in the actual graph, where n is the total number of vertices seen so far. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our distributed data structure, which we call the Forgiving Graph, has low latency and bandwidth requirements. The Forgiving Graph improves on the Forgiving Tree distributed data structure from Hayes et al. (2008) in the following ways: 1) it ensures low stretch over all pairs of nodes, while the Forgiving Tree only ensures low diameter increase; 2) it handles both node insertions and deletions, while the Forgiving Tree only handles deletions; 3) it requires only a very simple and minimal initialization phase, while the Forgiving Tree initially requires construction of a spanning tree of the network.

The Forgiving Graph:A distributed data structure for low stretch under adversarial attack

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick "repairs," which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions,without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes v and w whose distance would have been - in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most - log n in the actual graph, where n is the total number of vertices seen so far. Similarly, at any point, a node v whose degreewould have been d in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our distributed data structure, which we call the Forgiving Graph, has low latency and bandwidth requirements. The Forgiving Graph improves on the Forgiving Tree distributed data structure from Hayes et al. (2008) in the following ways: 1) it ensures low stretch over all pairs of nodes, while the Forgiving Tree only ensures low diameter increase; 2) it handles both node insertions and deletions, while the Forgiving Tree only handles deletions; 3) it requires only a very simple and minimal initialization phase, while the Forgiving Tree initially requires construction of a spanning tree of the network. © Springer-Verlag 2012.

Sublinear bounds for randomized leader election

This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) uses only O(√ √nlog^3/2n) messages to elect a unique leader (with high probability). When considering the "explicit" variant of leader election where eventually every node knows the identity of the leader, our algorithm yields the asymptotically optimal bounds of O(1) rounds and O(. n) messages. This algorithm is then extended to one solving leader election on any connected non-bipartite n-node graph G in O(τ(. G)) time and O(τ(G)n√log^3/2n) messages, where τ(. G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficient deterministic leader election algorithms. Finally, we present an almost matching lower bound for randomized leader election, showing that Ω(n) messages are needed for any leader election algorithm that succeeds with probability at least 1/. e+. ε, for any small constant ε. >. 0. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.

Properties of two interlinked Chi(2) interactions in noncollinear phase matching

We present a compact experimental realization of the interaction among five field modes in a chi((2)) nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. A peculiar behavior appears that has been experimentally verified. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal. (C) 2004 Optical Society of America

Macroscopic bound entanglement in thermal graph states

We address the presence of bound entanglement in strongly interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one- and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.

Ecological impacts of invasive alien species along temperature gradients: testing the role of environmental matching

Invasive alien species (IAS) can cause substantive ecological impacts, and the role of temperature in mediating these impacts may become increasingly significant in a changing climate. Habitat conditions and physiological optima offer predictive information for IAS impacts in novel environments. Here, using meta-analysis and laboratory experiments, we tested the hypothesis that the impacts of IAS in the field are inversely correlated with the difference in their ambient and optimal temperatures. A meta-analysis of 29 studies of consumptive impacts of IAS in inland waters revealed that the impacts of fishes and crustaceans are higher at temperatures that more closely match their thermal growth optima. In particular, the maximum impact potential was constrained by increased differences between ambient and optimal temperatures, as indicated by the steeper slope of a quantile regression on the upper 25th percentile of impact data compared to that of a weighted linear regression on all data with measured variances. We complemented this study with an experimental analysis of the functional response - the relationship between predation rate and prey supply - of two invasive predators (freshwater mysid shrimp, Hemimysis anomala and Mysis diluviana) across relevant temperature gradients; both of these species have previously been found to exert strong community-level impacts that are corroborated by their functional responses to different prey items. The functional response experiments showed that maximum feeding rates of H. anomala and M. diluviana have distinct peaks near their respective thermal optima. Although variation in impacts may be caused by numerous abiotic or biotic habitat characteristics, both our analyses point to temperature as a key mediator of IAS impact levels in inland waters and suggest that IAS management should prioritize habitats in the invaded range that more closely match the thermal optima of targeted invaders.