Self-Organizing Flows in Social Networks

Social networks offer users new means of accessing information, essentially relying on "social filtering", i.e. propagation and filtering of information by social contacts. The sheer amount of data flowing in these networks, combined with the limited budget of attention of each user, makes it difficult to ensure that social filtering brings relevant content to the interested users. Our motivation in this paper is to measure to what extent self-organization of the social network results in efficient social filtering. To this end we introduce flow games, a simple abstraction that models network formation under selfish user dynamics, featuring user-specific interests and budget of attention. In the context of homogeneous user interests, we show that selfish dynamics converge to a stable network structure (namely a pure Nash equilibrium) with close-to-optimal information dissemination. We show in contrast, for the more realistic case of heterogeneous interests, that convergence, if it occurs, may lead to information dissemination that can be arbitrarily inefficient, as captured by an unbounded "price of anarchy". Nevertheless the situation differs when users' interests exhibit a particular structure, captured by a metric space with low doubling dimension. In that case, natural autonomous dynamics converge to a stable configuration. Moreover, users obtain all the information of interest to them in the corresponding dissemination, provided their budget of attention is logarithmic in the size of their interest set

Complexity Results on Election of Multipoint Relays in Wireless Networks

The election of multipoint relays allows to decrease the cost of broadcasting in wireless networks. For each source, the fewer elements the set has, the greater the gain is. In this paper, we prove that the computation of a multipoint relay set with minimal size is NP-complete. We also make the analysis of a heuristic proposed by A. Qayyum

LiveRank: How to Refresh Old Datasets

This paper considers the problem of refreshing a dataset. More precisely , given a collection of nodes gathered at some time (Web pages, users from an online social network) along with some structure (hyperlinks, social relationships), we want to identify a significant fraction of the nodes that still exist at present time. The liveness of an old node can be tested through an online query at present time. We call LiveRank a ranking of the old pages so that active nodes are more likely to appear first. The quality of a LiveRank is measured by the number of queries necessary to identify a given fraction of the active nodes when using the LiveRank order. We study different scenarios from a static setting where the Liv-eRank is computed before any query is made, to dynamic settings where the LiveRank can be updated as queries are processed. Our results show that building on the PageRank can lead to efficient LiveRanks, for Web graphs as well as for online social networks

Average Size of Unstretched Remote-Spanners

International audienceMotivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remote-spanner. Given an unweighted graph $G$, a remote spanner is a set of links $H$ such that for any pair of nodes $(u,v)$ there exists a shortest path in $G$ for which all links in the path that are not adjacent to $u$ belong to $H$. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to $k$-connected graphs by considering minimum length sum over $k$ disjoint paths as distance. In this paper, we give distributed algorithms for computing remote-spanners in order to obtain sparse remote-spanners with various properties. We provide a polynomial distributed algorithm that computes a $k$-connecting unstretched remote-spanner whose number of edges is at a factor $2(1+\log \Delta)$ from optimal where $\Delta$ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O(\frackn\log n) in Erdös-Rényi graph model and O((\frackn)^\frac23) in the unit disk graph model with a uniform Poisson distribution of nodes

Remote spanners: what to know beyond neighbors

International audienceMotivated by the fact that neighbors are generally known in practical routing algorithms, we introduce the notion of remote-spanner. Given an unweighted graph $G$, a sub-graph $H$ with vertex set $V(H)=V(G)$ is an \emph{(\a,\b)-remote-spanner} if for each pair of points $u$ and $v$ the distance between $u$ and $v$ in $H_u$, the graph $H$ augmented by all the edges between $u$ and its neighbors in $G$, is at most \a times the distance between $u$ and $v$ in $G$ plus \b. We extend this definition to $k$-connected graphs by considering minimum length sum over $k$ disjoint paths as distance. We then say that an (\a,\b)-remote-spanner is \emph{$k$-connecting }. In this paper, we give distributed algorithms for computing (1+\eps,1-2\eps)-remote-spanners for any \eps>0, $k$-connecting $(1,0)$-remote-spanners for any $k\ge 1$ (yielding $(1,0)$-remote-spanners for $k=1$) and $2$-connecting $(2,-1)$-remote-spanners. All these algorithms run in constant time for any unweighted input graph. The number of edges obtained for $k$-connecting $(1,0)$-remote-spanner is within a logarithmic factor from optimal (compared to the best $k$-connecting $(1,0)$-remote-spanner of the input graph). Interestingly, sparse $(1,0)$-remote-spanners (i.e. preserving exact distances) with $O(n^4/3)$ edges exist in random unit disk graphs. The number of edges obtained for (1+\eps,1-2\eps)-remote-spanners and $2$-connecting $(2,-1)$-remote-spanners is linear if the input graph is the unit ball graph of a doubling metric (distances between nodes are unknown). Our methodology consists in characterizing remote-spanners as sub-graphs containing the union of small depth tree sub-graphs dominating nearby nodes. This leads to simple local distributed algorithms

Overhead in Mobile Ad-hoc Network Protocols

The present note proposes a survey of protocol overheads in mobile ad-hoc networks. An analysis is proposed to estimate overhead due to control packets. An analysis and simulations are proposed to estimate overhead due to non-optimality of the routes constructed by some protocols

Bi-connexité, k-connexité et multipoints relais

National audienceLes multipoints relais ont été introduits pour optimiser l'inondation dans un réseau ad hoc. Ils servent aussi, dans le protocole OLSR, à déterminer une sous-topologie qui conserve les plus courts chemin. Nous montrons, comment une généralisation des multipoints relais permet d'obtenir une sous-topologie conservant des propriétés de bi-connexité et plus généralement de k-connexité. Nous montrons de plus, que cette structure de multipoints relais est intrinsèque à toute sous-topologie montrant les mêmes propriétés

A Note on Models, Algorithms, and Data Structures for Dynamic Communication Networks

New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. Modeling such dynamics, and designing algorithms that take it into account, received considerable attention recently. In this note, we discuss a formal generalization of dynamic graphs, the evolving graphs, which aims at harnessing the complexity of an evolving setting as yielded by dynamic communication networks. We argue that evolving graphs are of great help when dealing with fixed-schedule networks. Moreover, we show how to exploit our model with networks where short time prediction is available

Computing Temporal Reachability Under Waiting-Time Constraints in Linear Time

This paper proposes a simple algorithm for computing single-source reachability in a temporal graph under waiting-time constraints, that is when waiting at each node is bounded by some time constraints. Given a space-time representation of a temporal graph, and a source node, the algorithm computes in linear-time which nodes and temporal edges are reachable through a constrained temporal walk from the source