Grid spanners with low forwarding index for energy efficient networks

International audienceA routing R of a connected graph G is a collection that contains simple paths connecting every ordered pair of vertices in G. The edge-forwarding index with respect to R (or simply the forwarding index with respect to $R) π(G, R)$ of G is the maximum number of paths in R passing through any edge of G. The forwarding index $π(G)$ of G is the minimum $π(G, R)$ over all routings R's of G. This parameter has been studied for different graph classes (1), (2), (3), (4). Motivated by energy efficiency, we look, for different numbers of edges, at the best spanning graphs of a square grid, namely those with a low forwarding index

Grid spanners with low forwarding index for energy efficient networks

International audienceA routing R of a connected graph G is a collection that contains simple paths connecting every ordered pair of vertices in G. The edge-forwarding index with respect to R (or simply the forwarding index with respect to R) π(G, R) of G is the maximum number of paths in R passing through any edge of G. The forwarding index π(G) of G is the minimum π(G, R) over all routings R's of G. This parameter has been studied for different graph classes [12], [1], [5], [4]. Motivated by energy efficiency, we look, for different numbers of edges, at the best spanning graphs of a square grid, namely those with a low forwarding index

Energy Efficient Routing by Switching-Off Network Interfaces

International audienceSeveral studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... The goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. In this paper, we consider a simplified architecture where a connection between two routers is represented as a link joining two network interfaces. When a connection is not used, both network interfaces can be turned off. Therefore, in order to reduce power consumption, the goal is to find the routing that minimizes the number of used links while satisfying all the demands. We first define formally the problem and we model it as an integer linear program. Then, we prove that this problem is not in APX, that is there is no polynomial-time constant-factor approximation algorithm. We propose a heuristic algorithm for this problem and we also prove some negative results about basic greedy and probabilistic algorithms. Thus we present a study on specific topologies, such as trees, grids and complete graphs, that provide bounds and results useful for real topologies. We then exhibit the gain in terms of number of network interfaces (leading to a global reduction of approximately 33 MWh for a medium-sized backbone network) for a set of existing network topologies: we see that for almost all topologies more than one third of the network interfaces can be spared for usual ranges of operation. Finally, we discuss the impact of energy efficient routing on the stretch factor and on fault tolerance.L'économie d'énergie dans les réseaux peut être accomplie en utilisant des techniques efficaces de routage ou de conception de réseaux. Dans ce papier, nous étudions une architecture simplifiée de réseaux dans laquelle lorsque deux routeurs sont reliés par un lien, les deux équipements extrémités de ce lien doivent être allumés. Chaque équipement ayant une consommation dépendant plutôt de son activation que de la quantité de traffic, notre objectif est de minimiser le nombre total d'équipements réseaux activés. Autrement dit, ce problème revient à effectuer un routage des demandes en minimisant le nombre d'arêtes dans la topologie. Nous proposons un programme linéaire pour résoudre ce problème et montrons des bornes simples sur des topologies particulières telles que la grille, l'arbre ou le graphe complet. Nous montrons des résultats d'inapproximabilité de ce problème, même si l'on considère des instances particulières. Nous proposons ensuite une heuristique dont nous évaluons les performances à l'aide de simulations sur des topologies réelles et sur la grille. Nous étudions ensuite l'impact de ces solutions efficaces en énergie sur la tolérance aux pannes et sur la longueur moyenne des routes. Finalement, nous proposons des structures de routage qui garantissent deux chemins disjoints par demande, ainsi qu'une limite sur la longueur des chemins

How to design graphs with low forwarding index and limited number of edges

International audienceThe (edge) forwarding index of a graph is the minimum, over all possible rout-ings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆, D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. For instance, we provide an asymptotically optimal construction for (n, n + k) cubic graphs-its forwarding index is ∼ n 2 3k log 2 (k). Our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected

Effective algorithms and protocols for wireless networking: a topological approach

Much research has been done on wireless sensor networks. However, most protocols and algorithms for such networks are based on the ideal model Unit Disk Graph (UDG) model or do not assume any model. Furthermore, many results assume the knowledge of location information of the network. In practice, sensor networks often deviate from the UDG model significantly. It is not uncommon to observe stable long links that are more than five times longer than unstable short links in real wireless networks. A more general network model, the quasi unit-disk graph (quasi-UDG) model, captures much better the characteristics of wireless networks. However, the understanding of the properties of general quasi-UDGs has been very limited, which is impeding the design of key network protocols and algorithms. In this dissertation we study the properties for general wireless sensor networks and develop new topological/geometrical techniques for wireless sensor networking. We assume neither the ideal UDG model nor the location information of the nodes. Instead we work on the more general quasi-UDG model and focus on figuring out the relationship between the geometrical properties and the topological properties of wireless sensor networks. Based on such relationships we develop algorithms that can compute useful substructures (planar subnetworks, boundaries, etc.). We also present direct applications of the properties and substructures we constructed including routing, data storage, topology discovery, etc. We prove that wireless networks based on quasi-UDG model exhibit nice properties like separabilities, existences of constant stretch backbones, etc. We develop efficient algorithms that can obtain relatively dense planar subnetworks for wireless sensor networks. We also present efficient routing protocols and balanced data storage scheme that supports ranged queries. We present algorithmic results that can also be applied to other fields (e.g., information management). Based on divide and conquer and improved color coding technique, we develop algorithms for path, matching and packing problem that significantly improve previous best algorithms. We prove that it is unlikely for certain problems in operation science and information management to have any relatively effective algorithm or approximation algorithm for them

Unified Power Management in Wireless Sensor Networks, Doctoral Dissertation, August 2006

Radio power management is of paramount concern in wireless sensor networks (WSNs) that must achieve long lifetimes on scarce amount of energy. Previous work has treated communication and sensing separately, which is insufficient for a common class of sensor networks that must satisfy both sensing and communication requirements. Furthermore, previous approaches focused on reducing energy consumption in individual radio states resulting in suboptimal solutions. Finally, existing power management protocols often assume simplistic models that cannot accurately reflect the sensing and communication properties of real-world WSNs. We develop a unified power management approach to address these issues. We first analyze the relationship between sensing and communication performance of WSNs. We show that sensing coverage often leads to good network connectivity and geographic routing performance, which provides insights into unified power management under both sensing and communication performance requirements. We then develop a novel approach called Minimum Power Configuration that ingegrates the power consumption in different radio states into a unified optimization framework. Finally, we develop two power management protocols that account for realistic communication and sensing properties of WSNs. Configurable Topology Control can configure a network topology to achieve desired path quality in presence of asymmetric and lossy links. Co-Grid is a coverage maintenance protocol that adopts a probabilistic sensing model. Co-Grid can satisfy desirable sensing QoS requirements (i.e., detection probability and false alarm rate) based on a distributed data fusion model

Recent Trends in Communication Networks

In recent years there has been many developments in communication technology. This has greatly enhanced the computing power of small handheld resource-constrained mobile devices. Different generations of communication technology have evolved. This had led to new research for communication of large volumes of data in different transmission media and the design of different communication protocols. Another direction of research concerns the secure and error-free communication between the sender and receiver despite the risk of the presence of an eavesdropper. For the communication requirement of a huge amount of multimedia streaming data, a lot of research has been carried out in the design of proper overlay networks. The book addresses new research techniques that have evolved to handle these challenges

Algorithms for Triangles, Cones & Peaks

Three different geometric objects are at the center of this dissertation: triangles, cones and peaks. In computational geometry, triangles are the most basic shape for planar subdivisions. Particularly, Delaunay triangulations are a widely used for manifold applications in engineering, geographic information systems, telecommunication networks, etc. We present two novel parallel algorithms to construct the Delaunay triangulation of a given point set. Yao graphs are geometric spanners that connect each point of a given set to its nearest neighbor in each of $k$ cones drawn around it. They are used to aid the construction of Euclidean minimum spanning trees or in wireless networks for topology control and routing. We present the first implementation of an optimal $\mathcal{O}(n \log n)$-time sweepline algorithm to construct Yao graphs. One metric to quantify the importance of a mountain peak is its isolation. Isolation measures the distance between a peak and the closest point of higher elevation. Computing this metric from high-resolution digital elevation models (DEMs) requires efficient algorithms. We present a novel sweep-plane algorithm that can calculate the isolation of all peaks on Earth in mere minutes