Construction of Quality Virtual Backbones with Link Fault Tolerance in Wireless Sensor Networks

Wireless sensor networks (WSNs) are extensively utilized in various circumstances. For applications, the construction of the virtual backbones (VBs) of WSNs has attracted considerable attention in this field. Generally, a homogeneous WSN is formulated as a unit disk graph (UDG), and the VB of the corresponding WSN is modeled as a connected dominating set (CDS) in the UDG. In certain applications, communication between sensors in a network may fail for various reasons, such as sensor movement, signal interference, and the appearance of obstacles. Consequently, a CDS in a UDG should possess fault tolerance on the edges. In this paper, we introduce a new concept called the 2 edge-connected 2 edge-dominating set ( 2 , 2 -ECDS); then, we design an approximation algorithm for computing 2 , 2 -ECDSs in UDGs, the performance ratio of which is 30.51. By means of simulations, we compare our algorithm and existing algorithms in terms of the CDS size, running time, success rate, and network lifetime. The simulation results indicate that our algorithm exhibits better performance and is more suitable for constructing a VB with edge fault tolerance in a WSN.

Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis

We seek to quantify the extent of similarity among nodes in a complex network with respect to two or more node-level metrics (like centrality metrics). In this pursuit, we propose the following unit disk graph-based approach: we first normalize the values for the node-level metrics (using the sum of the squares approach) and construct a unit disk graph of the network in a coordinate system based on the normalized values of the node-level metrics. There exists an edge between two vertices in the unit disk graph if the Euclidean distance between the two vertices in the normalized coordinate system is within a threshold value (ranging from 0 tok, where k is the number of node-level metrics considered). We run a binary search algorithm to determine the minimum value for the threshold distance that would yield a connected unit disk graph of the vertices. We refer to “1 − (minimum threshold distance/k)” as the node similarity index (NSI; ranging from 0 to 1) for the complex network with respect to the k node-level metrics considered. We evaluate the NSI values for a suite of 60 real-world networks with respect to both neighborhood-based centrality metrics (degree centrality and eigenvector centrality) and shortest path-based centrality metrics (betweenness centrality and closeness centrality).

An Efficient Search Algorithm for Multi-hop Network Localization in a Sparse Unit Disk Graph Model

We consider a network localization problem by modeling this as a unit disk graph where nodes are randomly placed with uniform distribution in an area.The connectivity between nodes is defined when the distances fall within a unit range. Under a condition that certain nodes know their locations (anchor nodes), this paper proposes a heuristic approach to find a realization for the rest of the network by applying a tree search algorithm in a depth- first search manner. Our contribution is to put together a priori information and constraints such as graph properties in order to speed up the search. An evaluation function is formed and used to prune down the search space. This evaluation function is used to select the order of the unknown nodes to iterate. This paper also extends the idea further by accommodating a variety of other properties of graphs into the evaluation function. The results show that node degrees, node distances and shortest paths to anchor nodes drastically reduce the number of iterations required for realizing a feasible localization instance both in noise-free and noisy environments. Finally, some preliminary complexity analysis is also given.