Signed graph embedding: when everybody can sit closer to friends than enemies

Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions, recent empirical studies have proved that they fail to reflect some current practices in real social networks. In this paper we address the issue of drawing signed graphs and capturing such social interactions. We relax the previous assumptions to define a drawing as a model in which every vertex has to be placed closer to its neighbors connected via a positive edge than its neighbors connected via a negative edge in the resulting space. Based on this definition, we address the problem of deciding whether a given signed graph has a drawing in a given $\ell$-dimensional Euclidean space. We present forbidden patterns for signed graphs that admit the introduced definition of drawing in the Euclidean plane and line. We then focus on the $1$-dimensional case, where we provide a polynomial time algorithm that decides if a given complete signed graph has a drawing, and constructs it when applicable

Connectivity-guaranteed and obstacle-adaptive deployment schemes for mobile sensor networks

Mobile sensors can relocate and self-deploy into a network. While focusing on the problems of coverage, existing deployment schemes largely over-simplify the conditions for network connectivity: they either assume that the communication range is large enough for sensors in geometric neighborhoods to obtain location information through local communication, or they assume a dense network that remains connected. In addition, an obstacle-free field or full knowledge of the field layout is often assumed. We present new schemes that are not governed by these assumptions, and thus adapt to a wider range of application scenarios. The schemes are designed to maximize sensing coverage and also guarantee connectivity for a network with arbitrary sensor communication/sensing ranges or node densities, at the cost of a small moving distance. The schemes do not need any knowledge of the field layout, which can be irregular and have obstacles/holes of arbitrary shape. Our first scheme is an enhanced form of the traditional virtual-force-based method, which we term the Connectivity-Preserved Virtual Force (CPVF) scheme. We show that the localized communication, which is the very reason for its simplicity, results in poor coverage in certain cases. We then describe a Floor-based scheme which overcomes the difficulties of CPVF and, as a result, significantly outperforms it and other state-of-the-art approaches. Throughout the paper our conclusions are corroborated by the results from extensive simulations

Ordered slicing of very large-scale overlay networks

Climate change is expected to have a large impact on northern ecosystems. Increased temperatures and altered precipitation and snow cover patterns will have a great impact on subarctic tundra. Bryophytes form an important component of tundra ecosystems because of their high abundance and their importance in many ecological processes. The effect of elevation and snow cover on freezing damage in shoots of three subarctic bryophytes: Ptilidium ciliare, Hylocomium splendens and Sphagnum fuscum, was studied in a snow manipulation field experiment at different elevations in Abisko, Sweden, during early spring. The treatments included snow addition, snow removal and control. In addition, bryophyte healthiness at the plot scale was determined by image analysis using colour selection, and soil temperature and moisture data were collected. Freezing damage differed significantly among bryophyte species with P. ciliare having the lowest freezing damage. There was a decrease in freezing damage over time due to the increase in temperature as spring progressed. Counter expectation, freezing damage was higher at low elevation although the mean daily minimum temperature was lower at higher elevation, which might be due to adaptation effects. Snow treatment had only a minor effect on freezing damage, but it did have an effect on proportion of undamaged tissue at the plot scale which increased with increasing snow cover at high elevation, but decreased with increasing snow cover at low elevation. Soil moisture content was also affected by snow treatment. The number of freeze-thaw cycles was less for S. fuscum and H. splendens compared to bare soil plots, which indicates insulating capacities of these bryophytes. Freezing damage could not be explained by the measured climate variables alone; therefore, it is likely the result of a complex set of factors, possibly including solar radiation and disturbance by herbivores

Bounds on the Voter Model in Dynamic Networks

In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes have the same opinion. We consider dynamic graphs in which the edges are rewired in every round (by an adversary) giving rise to the graph sequence $G_1, G_2, \dots$, where we assume that $G_i$ has conductance at least $\phi_i$. We assume that the degrees of nodes don't change over time as one can show that the consensus time can become super-exponential otherwise. In the case of a sequence of $d$-regular graphs, we obtain asymptotically tight results. Even for some static graphs, such as the cycle, our results improve the state of the art. Here we show that the expected number of rounds until all nodes have the same opinion is bounded by $O(m/(d_{min} \cdot \phi))$, for any graph with $m$ edges, conductance $\phi$, and degrees at least $d_{min}$. In addition, we consider a biased dynamic voter model, where each opinion $i$ is associated with a probability $P_i$, and when a node chooses a neighbour with that opinion, it adopts opinion $i$ with probability $P_i$ (otherwise the node keeps its current opinion). We show for any regular dynamic graph, that if there is an $\epsilon>0$ difference between the highest and second highest opinion probabilities, and at least $\Omega(\log n)$ nodes have initially the opinion with the highest probability, then all nodes adopt w.h.p. that opinion. We obtain a bound on the convergences time, which becomes $O(\log n/\phi)$ for static graphs

Scalable and Secure Aggregation in Distributed Networks

We consider the problem of computing an aggregation function in a \emph{secure} and \emph{scalable} way. Whereas previous distributed solutions with similar security guarantees have a communication cost of $O(n^3)$, we present a distributed protocol that requires only a communication complexity of $O(n\log^3 n)$, which we prove is near-optimal. Our protocol ensures perfect security against a computationally-bounded adversary, tolerates $(1/2-\epsilon)n$ malicious nodes for any constant $1/2 > \epsilon > 0$ (not depending on $n$), and outputs the exact value of the aggregated function with high probability

The Out-of-core KNN Awakens: The light side of computation force on large datasets

International audienceK-Nearest Neighbors (KNN) is a crucial tool for many applications , e.g. recommender systems, image classification and web-related applications. However, KNN is a resource greedy operation particularly for large datasets. We focus on the challenge of KNN computation over large datasets on a single commodity PC with limited memory. We propose a novel approach to compute KNN on large datasets by leveraging both disk and main memory efficiently. The main rationale of our approach is to minimize random accesses to disk, maximize sequential accesses to data and efficient usage of only the available memory. We evaluate our approach on large datasets, in terms of performance and memory consumption. The evaluation shows that our approach requires only 7% of the time needed by an in-memory baseline to compute a KNN graph

Peer to peer multidimensional overlays: Approximating complex structures

Peer to peer overlay networks have proven to be a good support for storing and retrieving data in a fully decentralized way. A sound approach is to structure them in such a way that they reflect the structure of the application. Peers represent objects of the application so that neighbours in the peer to peer network are objects having similar characteristics from the application's point of view. Such structured peer to peer overlay networks provide a natural support for range queries. While some complex structures such as a Voronoï tessellation, where each peer is associated to a cell in the space, are clearly relevant to structure the objects, the associated cost to compute and maintain these structures is usually extremely high for dimensions larger than 2. We argue that an approximation of a complex structure is enough to provide a native support of range queries. This stems fromthe fact that neighbours are importantwhile the exact space partitioning associated to a given peer is not as crucial. In this paper we present the design, analysis and evaluation of RayNet, a loosely structured Voronoï-based overlay network. RayNet organizes peers in an approximation of a Voronoï tessellation in a fully decentralized way. It relies on a Monte-Carlo algorithm to estimate the size of a cell and on an epidemic protocol to discover neighbours. In order to ensure efficient (polylogarithmic) routing, RayNet is inspired from the Kleinberg's small world model where each peer gets connected to close neighbours (its approximate Voronoï neighbours in Raynet) and shortcuts, long range neighbours, implemented using an existing Kleinberg-like peer sampling