Xheal: A localized self-healing algorithm using expanders

We consider the problem of self-healing in reconfigurable networks e.g., peer-to-peer and wireless mesh networks. For such networks under repeated attack by an omniscient adversary, we propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, while keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Xheal has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] andForgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.

Dense subgraphs on dynamic networks

In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense substructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might reveal community clusters or dense regions for possibly maintaining good communication infrastructure. In this work, we address the problem of self-awareness of nodes in a dynamic network with regards to graph density, i.e., we give distributed algorithms for maintaining dense subgraphs that the member nodes are aware of. The only knowledge that the nodes need is that of the dynamic diameter D, i.e., the maximum number of rounds it takes for a message to traverse the dynamic network. For our work, we consider a model where the number of nodes are fixed, but a powerful adversary can add or remove a limited number of edges from the network at each time step. The communication is by broadcast only and follows the CONGEST model. Our algorithms are continuously executed on the network, and at any time (after some initialization) each node will be aware if it is part (or not) of a particular dense subgraph. We give algorithms that (2 + e)-approximate the densest subgraph and (3 + e)-approximate the at-least-k-densest subgraph (for a given parameter k). Our algorithms work for a wide range of parameter values and run in O(D log n) time. Further, a special case of our results also gives the first fully decentralized approximation algorithms for densest and at-least-k-densest subgraph problems for static distributed graphs. © 2012 Springer-Verlag.

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.

Investigation of AIMD based charging strategies for EVs connected to a low-voltage distribution network

In this paper we consider charging strategies that mitigate the impact of domestic charging of EVs on low-voltage distribution networks and which seek to reduce peak power by responding to time-ofday pricing. The strategies are based on the distributed Additive Increase and Multiplicative Decrease (AIMD) charging algorithms proposed in [5]. The strategies are evaluated using simulations conducted on a custom OpenDSS-Matlab platform for a typical low voltage residential feeder network. Results show that by using AIMD based smart charging 50% EV penetration can be accommodated on our test network, compared to only 10% with uncontrolled charging, without needing to reinforce existing network infrastructure. © Springer-Verlag Berlin Heidelberg 2013.

DEX: Self-Healing Expanders

We present a fully-distributed self-healing algorithm DEX, that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders - whose expansion properties hold deterministically - that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only probabilistic guarantees on the network expansion which rapidly degrade in a dynamic setting, in particular, the expansion properties can degrade even more rapidly under adversarial insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only O(log n) rounds and O(log n) messages are needed with high probability (n is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table (DHT) on top of DEX, with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have guaranteed properties (constant bounded degree and expansion) despite dynamic changes.

On the Complexity of Universal Leader Election

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This article focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most "obvious" complexity bounds have not been proven for randomized algorithms. In particular, the seemingly obvious lower bounds of Ω(m) messages, where m is the number of edges in the network, and Ω(D) time, where D is the network diameter, are nontrivial to show for randomized (Monte Carlo) algorithms. (Recent results, showing that even Ω(n), where n is the number of nodes in the network, is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms, except for the restricted case of comparison algorithms, where it was also required that nodes may not wake up spontaneously and that D and n were not known. We establish these fundamental lower bounds in this article for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (namely, algorithms that work for all graphs), apply to every D, m, and n, and hold even if D, m, and n are known, all the nodes wake up simultaneously, and the algorithms can make any use of node's identities. To show that these bounds are tight, we present an O(m) messages algorithm. An O(D) time leader election algorithm is known. A slight adaptation of our lower bound technique gives rise to an Ω(m) message lower bound for randomized broadcast algorithms. 

An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. The answer is known to be negative in the deterministic setting. We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that tradeoff messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.

Comparison of a centralised and distributed approach for a generic scheduling system

PEGS (Production and Environmental Generic Scheduler) is a generic production scheduler that produces good schedules over a wide range of problems. It is centralised, using search strategies with the Shifting Bottleneck algorithm. We have also developed an alternative distributed approach using software agents. In some cases this reduces run times by a factor of 10 or more. In most cases, the agent-based program also produces good solutions for published benchmark data, and the short run times make our program useful for a large range of problems. Test results show that the agents can produce schedules comparable to the best found so far for some benchmark datasets and actually better schedules than PEGS on our own random datasets. The flexibility that agents can provide for today's dynamic scheduling is also appealing. We suggest that in this sort of generic or commercial system, the agent-based approach is a good alternative.

Swarm scheduling approaches for work-flow applications with security constraints in distributed data-intensive computing environments

The scheduling problem in distributed data-intensive computing environments has become an active research topic due to the tremendous growth in grid and cloud computing environments. As an innovative distributed intelligent paradigm, swarm intelligence provides a novel approach to solving these potentially intractable problems. In this paper, we formulate the scheduling problem for work-flow applications with security constraints in distributed data-intensive computing environments and present a novel security constraint model. Several meta-heuristic adaptations to the particle swarm optimization algorithm are introduced to deal with the formulation of efficient schedules. A variable neighborhood particle swarm optimization algorithm is compared with a multi-start particle swarm optimization and multi-start genetic algorithm. Experimental results illustrate that population based meta-heuristics approaches usually provide a good balance between global exploration and local exploitation and their feasibility and effectiveness for scheduling work-flow applications. © 2010 Elsevier Inc. All rights reserved.

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.

EEG decoding of semantic category reveals distributed representations for single concepts

Achieving a clearer picture of categorial distinctions in the brain is essential for our understanding of the conceptual lexicon, but much more fine-grained investigations are required in order for this evidence to contribute to lexical research. Here we present a collection of advanced data-mining techniques that allows the category of individual concepts to be decoded from single trials of EEG data. Neural activity was recorded while participants silently named images of mammals and tools, and category could be detected in single trials with an accuracy well above chance, both when considering data from single participants, and when group-training across participants. By aggregating across all trials, single concepts could be correctly assigned to their category with an accuracy of 98%. The pattern of classifications made by the algorithm confirmed that the neural patterns identified are due to conceptual category, and not any of a series of processing-related confounds. The time intervals, frequency bands and scalp locations that proved most informative for prediction permit physiological interpretation: the widespread activation shortly after appearance of the stimulus (from 100. ms) is consistent both with accounts of multi-pass processing, and distributed representations of categories. These methods provide an alternative to fMRI for fine-grained, large-scale investigations of the conceptual lexicon. © 2010 Elsevier Inc.

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.

Distribution Network Voltage Support Using Sensitivity-based Dispatch of Distributed Generation

This paper is concerned with the voltage and reactive power issues surrounding the connection of Distributed Generation (DG) on the low-voltage (LV) distribution network. The presented system-wide voltage control algorithm consists of three stages. Firstly available reactive power reserves are utilized. Then, if required, DG active power output is curtailed. Finally, curtailment of non-critical site demand is considered. The control methodology is tested on a variant of the 13-bus IEEE Node Radial Distribution Test Feeder. The presented control algorithm demonstrated that the distribution system operator (DSO) can maintain voltage levels within a desired statutory range by dispatching reactive power from DG or network devices. The practical application of the control strategy is discussed.

Distributed Consensus Charging for Current Unbalance Reduction

Electric Vehicle (EV) technology has developed rapidly in recent years, with the result that increasing levels of EV penetration are expected on electrical grids in the near future. The increasing electricity demand due to EVs is expected to provide many challenges for grid companies, and it is expected that it will be necessary to reinforce the current electrical grid infrastructure to cater for increasing loads at distribution level. However, by harnessing the power of Vehicle to Grid (V2G) technologies, groups of EVs could be harnessed to provide ancillary services to the grid. Current unbalance occurs at distribution level when currents are unbalanced between each of the phases. In this paper a distributed consensus algorithm is used to coordinate EV charging in order to minimise current unbalance. Simulation results demonstrate that the proposed algorithm is effective in rebalancing phase currents.

Enabling Robust and Efficient Distributed Computation in Dynamic Peer-to-Peer Networks

Motivated by the need for designing efficient and robust fully-distributed computation in highly dynamic networks such as Peer-to-Peer (P2P) networks, we study distributed protocols for constructing and maintaining dynamic network topologies with good expansion properties. Our goal is to maintain a sparse (bounded degree) expander topology despite heavy {\em churn} (i.e., nodes joining and leaving the network continuously over time). We assume that the churn is controlled by an 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. Our main contribution is a randomized distributed protocol that guarantees with high probability the maintenance of a {\em constant} degree graph with {\em high expansion} even under {\em continuous high adversarial} churn. Our protocol can tolerate a churn rate of up to $O(n/\poly\log(n))$ per round (where $n$ is the stable network size). Our protocol is efficient, lightweight, and scalable, and it incurs only $O(\poly\log(n))$ overhead for topology maintenance: only polylogarithmic (in $n$) bits needs to be processed and sent by each node per round and any node's computation cost per round is also polylogarithmic. The given protocol is a fundamental ingredient that is needed for the design of efficient fully-distributed algorithms for solving fundamental distributed computing problems such as agreement, leader election, search, and storage in highly dynamic P2P networks and enables fast and scalable algorithms for these problems that can tolerate a large amount of churn.