Extremal Properties of Three Dimensional Sensor Networks with Applications

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that $n$ nodes, each capable of sensing events within a radius of $r$, are randomly and uniformly distributed in a 3-dimensional region $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks

Joint multicast routing and channel assignment in multiradio multichannel wireless mesh networks using tabu search

Copyright @ 2009 IEEE Computer SocietyThis paper proposes a tabu search (TS) based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. The path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we expect the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the tabu search procedure are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed TS multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Joint multicast routing and channel assignment in multiradio multichannel wireless mesh networks using simulated annealing

This is the post-print version of the article - Copyright @ 2008 Springer-VerlagThis paper proposes a simulated annealing (SA) algorithm based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. In the proposed SA multicast algorithm, the path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we anticipate the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the annealing process are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed SA based multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem