On Fast and Robust Information Spreading in the Vertex-Congest Model

This paper initiates the study of the impact of failures on the fundamental problem of \emph{information spreading} in the Vertex-Congest model, in which in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message to all of its neighbors. Our contribution to coping with failures is twofold. First, we prove that the randomized algorithm which chooses uniformly at random the next message to forward is slow, requiring $\Omega(n/\sqrt{k})$ rounds on some graphs, which we denote by $G_{n,k}$, where $k$ is the vertex-connectivity. Second, we design a randomized algorithm that makes dynamic message choices, with probabilities that change over the execution. We prove that for $G_{n,k}$ it requires only a near-optimal number of $O(n\log^3{n}/k)$ rounds, despite a rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing probabilities that change according to the execution is of independent interest.Comment: Appears in SIROCCO 2015 conferenc

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Mathematical Foundations and Algorithms for Clique Relaxations in Networks

This dissertation establishes mathematical foundations for the properties exhibited by generalizations of cliques, as well as algorithms to find such objects in a network. Cliques are a model of an ideal group with roots in social network analysis. They have since found applications as a part of grouping mechanisms in computer vision, coding theory, experimental design, genomics, economics, and telecommunications among other fields. Because only groups with ideal properties form a clique, they are often too restrictive for identifying groups in many real-world networks. This motivated the introduction of clique relaxations that preserve some of the various defining properties of cliques in relaxed form. There are six clique relaxations that are the focus of this dissertation: s-clique, s-club, s-plex, k-core, quasi-clique, and k-connected subgraphs. Since cliques have found applications in so many fields, research into these clique relaxations has the potential to steer the course of much future research. The focus of this dissertation is on bringing organization and rigorous methodology to the formation and application of clique relaxations. We provide the first taxonomy focused on how the various clique relaxations relate on key structural properties demonstrated by groups. We also give a framework for how clique relaxations can be formed. This equips researchers with the ability to choose the appropriate clique relaxation for an application based on its structural properties, or, if an appropriate clique relaxation does not exist, form a new one. In addition to identifying the structural properties of the various clique relaxations, we identify properties and prove propositions that are important computationally. These assist in creating algorithms to find a clique relaxation quickly as it is immersed in a network. We give the first ever analysis of the computational complexity of finding the maximum quasi-clique in a graph. Such analysis identifies for researchers the appropriate set of computational tools to solve the maximum quasiclique problem. We further create a polynomial time algorithm for identifying large 2-cliques within unit disk graphs, a special class of graphs often arising in communication networks. We prove the algorithm to have a guaranteed 1=2-approximation ratio and finish with computational results

Association Control in Wireless Mesh Networks

Ph.DDOCTOR OF PHILOSOPH

Cross-layer design for network performance optimization in wireless networks

In this dissertation, I use mathematical optimization approach to solve the complex network problems. Paper l and paper 2 first show that ignoring the bandwidth constraint can lead to infeasible routing solutions. A sufficient condition on link bandwidth is proposed that makes a routing solution feasible, and then a mathematical optimization model based on this sufficient condition is provided. Simulation results show that joint optimization models can provide more feasible routing solutions and provide significant improvement on throughput and lifetime. In paper 3 and paper 4, an interference model is proposed and a transmission scheduling scheme is presented to minimize the end-to-end delay. This scheduling scheme is designed based on integer linear programming and involves interference modeling. Using this schedule, there are no conflicting transmissions at any time. Through simulation, it shows that the proposed link scheduling scheme can significantly reduce end-to-end latency. Since to compute the maximum throughput is an NP-hard problem, efficient heuristics are presented in Paper 5 that use sufficient conditions instead of the computationally-expensive-to-get optimal condition to capture the mutual conflict relation in a collision domain. Both one-way transmission and two-way transmission are considered. Simulation results show that the proposed algorithms improve network throughput and reduce energy consumption, with significant improvement over previous work on both aspects. Paper 6 studies the complicated tradeoff relation among multiple factors that affect the sensor network lifetime and proposes an adaptive multi-hop clustering algorithm. It realizes the best tradeoff among multiple factors and outperforms others that do not. It is adaptive in the sense the clustering topology changes over time in order to have the maximum lifetime --Abstract, page iv

Graph-theoretic channel modeling and topology control protocols for wireless sensor networks

This report addresses two different research problems: (i) It presents a wireless channel model that reduces the complexity associated with high order Markov chains; and (ii) presents energy efficient topology control protocols which provide reliability while maintaining the topology in an energy efficient manner. For the above problems, real wireless sensor network traces were collected and extensive simulations were performed for evaluating the proposed protocols. Accurate simulation and analysis of wireless networks are inherently dependent on accurate models which are able to provide real-time channel characterization. High-order Markov chains are typically used to model errors and losses over wireless channels. However, complexity (i.e., the number of states) of a high-order Markov model increases exponentially with the memory-length of the underlying channel. In this report, a novel graph-theoretic methodology that uses Hamiltonian circuits to reduce the complexity of a high-order Markov model to a desired state budget is presented. The implication of unused states in complexity reduction of higher order Markov model is also explained. The trace-driven performance evaluations for real wireless local area network (WLAN) and wireless sensor network (WSN) channels demonstrate that the proposed Hamiltonian Model, while providing orders of magnitude reduction in complexity, renders an accuracy that is comparable to the Markov model and better than the existing reduced state models. Furthermore, a methodology to preserve energy is presented to increase the network lifetime by reducing the node degree forming an active backbone while considering network connectivity. However, in energy stringent wireless sensor networks, it is of utmost importance to construct the reduced topology with the minimal control overhead. Moreover, most wireless links in practice are lossy links with connectivity probability which desires that a routing protocol provides routing flexibility and reliability at a minimum energy consumption cost. For this purpose, distributed and semi-distributed novel graph-theoretic topology construction protocols are presented that exploit cliques and polygons in a WSN to achieve energy efficiency and reliability. The proposed protocols also facilitate load rotation under topology maintenance, thereby extending the network lifetime. In addition to the above, the report also evaluates why the backbone construction using connected dominating set (CDS) in certain cases remains unable to provide connected sensing coverage in the area covered. For this purpose, a novel protocol that reduces the topology while considering sensing area coverage is presented

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende