Interference Minimization in Asymmetric Sensor Networks

A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the \emph{receiver interference}. This is modeled as follows: each sensor node corresponds to a point in $\mathbb{R}^d$ and each \emph{transmission range} corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radii that minimize the maximum interference while maintaining a strongly connected asymmetric communication graph. For the two-dimensional case, we show that it is NP-complete to decide whether one can achieve a receiver interference of at most $5$. In the one-dimensional case, we prove that there are optimal solutions with nontrivial structural properties. These properties can be exploited to obtain an exact algorithm that runs in quasi-polynomial time. This generalizes a result by Tan et al. to the asymmetric case.Comment: 15 pages, 5 figure

On interference among moving sensors and related problems

We show that for any set of $n$ points moving along "simple" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the points of size $O(k \log k)$, such that the Voronoi diagram of this subset is "balanced" at any given time (i.e., it contains $O(n/k)$ points per cell). We also show that the bound $O(k \log k)$ is near optimal even for the one dimensional case in which points move linearly in time. As applications, we show that one can assign communication radii to the sensors of a network of $n$ moving sensors so that at any given time their interference is $O(\sqrt{n\log n})$. We also show some results in kinetic approximate range counting and kinetic discrepancy. In order to obtain these results, we extend well-known results from $\varepsilon$-net theory to kinetic environments

A General Approach for Minimizing the Maximum Interference of a Wireless Ad-Hoc Network in Plane

The interference reduction is one of the most important problems in the field of wireless sensor networks. Wireless sensor network elements are small mobile receiver and transmitters. The energy of processor and other components of each device is supplied by a small battery with restricted energy. One of the meanings that play an important role in energy consumption is the interference of signals. The interference of messages through a wireless network, results in message failing and transmitter should resend its message, thus the interference directly affect on the energy consumption of transmitter. This paper presents an algorithm which suggests the best subgraph for the input distribution of the nodes in the plane how the maximum interference of the proposed graph has the minimum value. The input of the application is the complete network graph, which means we know the cost of each link in the network graph. Without any lose of generality the Euclidean distance could be used as the weight of each link. The links are arranged and ranked according to their weights, in an iterative process the link which imposition minimum increase on the network interference with some extra conditions which is proposed in future sections, is added to resulting topology and is eliminated from list until all nodes are connected together. Experimental results show the efficiency of proposed algorithm not only for one dimensional known distribution like exponential node chain, but also for two dimensional distributions like two Exponential node chains and alpha-Spiral node chains

Exact algorithms to minimize interference in wireless sensor networks

AbstractFinding a low-interference connected topology is a fundamental problem in wireless sensor networks (WSNs). The problem of reducing interference through adjusting the nodes’ transmission radii in a connected network is one of the most well-known open algorithmic problems in wireless sensor network optimization. In this paper, we study minimization of the average interference and the maximum interference for the highway model, where all the nodes are arbitrarily distributed on a line. First, we prove that there is always an optimal topology with minimum interference that is planar. Then, two exact algorithms are proposed. The first one is an exact algorithm to minimize the average interference in polynomial time, O(n3Δ), where n is the number of nodes and Δ is the maximum node degree. The second one is an exact algorithm to minimize the maximum interference in sub-exponential time, O(n3ΔO(k)), where k=O(Δ) is the minimum maximum interference. All the optimal topologies constructed are planar

Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

Consider $n$ mobile sensors placed randomly in $m-$dimensional unit cube for fixed $m\in\{1,2\}.$ The sensors have identical sensing range, say $r.$ We are interested in moving the sensors from their initial random positions to new locations so that every point in the unit cube is within the range of at least one sensor, while at the same time each pair of sensors is placed at interference distance greater or equal to $s.$ Suppose the displacement of the $i-$th sensor is a distance $d_i$. As a \textit{energy consumption} for the displacement of a set of $n$ sensors we consider the $a-$total displacement defined as the sum $\sum_{i=1}^n d_i^a,$ for some constant $a> 0.$ The main contribution of this paper can be summarized as follows. For the case of unit interval we \textit{explain a threshold} around the sensing radius equal to $\frac{1}{2n}$ and the interference distance equal to $\frac{1}{n}$ for the expected minimum $a-$total displacement. For the sensors placed in the unit square we \textit{explain a threshold} around the square sensing radius equal to $\frac{1}{2 \sqrt{n}}$ and the interference distance equal to $\frac{1}{\sqrt{n}}$ for the expected minimum $a-$total displacement