Scientific Programming

Volume 2017 (2017), Article ID 5807289, 19 pages

https://doi.org/10.1155/2017/5807289

## Hybrid Recovery Strategy Based on Random Terrain in Wireless Sensor Networks

^{1}School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China^{2}School of Online and Continuing Education, Fujian University of Technology, Fuzhou, China^{3}Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, China

Correspondence should be addressed to Li Xu

Received 17 April 2016; Revised 19 June 2016; Accepted 26 June 2016; Published 5 January 2017

Academic Editor: Dantong Yu

Copyright © 2017 Xiaoding Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Providing successful data collection and aggregation is a primary goal for a broad spectrum of critical applications of wireless sensor networks. Unfortunately, the problem of connectivity loss, which may occur when a network suffers from natural disasters or human sabotages, may cause failure in data aggregation. To tackle this issue, plenty of strategies that deploy relay devices on target areas to restore connectivity have been devised. However, all of them assume that either the landforms of target areas are flat or there are sufficient relay devices. In real scenarios, such assumptions are not realistic. In this paper, we propose a hybrid recovery strategy based on random terrain (simply, HRSRT) that takes both realistic terrain influences and quantitative limitations of relay devices into consideration. is proved to accomplish the biconnectivity restoration and meanwhile minimize the energy cost for data collection and aggregation. In addition, both of complexity and approximation ratio of are explored. The simulation results show that performs well in terms of overall/maximum energy cost.

#### 1. Introduction

Wireless sensor networks (s) have raised a great attention thanks to their vast spectrum of industrial and social applications [1, 2], such as biological detection, environment monitoring, and battlefield surveillance. Data collection and aggregation are the first priority of s. The primary objective of such task is to gather sensor readings from field sensors deployed over a geographic area (called the area of interest ()) and then successfully deliver all gathered data to the sink node through multihop paths [3]. That implies the importance of both connectivity maintenance and optimal network topologies discovery for s [4]. However, natural disasters and human sabotages will jeopardize the network connectivity so that the process of data aggregation will be compromised without doubt. For example, when a is carrying out a surveillance mission on the activity of a volcano, if the connectivity is lost, then all gathered data will not be able to reach the sink node for further analysis. Without such important data, volcano eruption can not be predicted. That may cause massive casualties and severe economic losses.

Due to the significance of network connectivity as mentioned above, the problem of connectivity restoration has been receiving increasing attention in recent years. Thus, it is imperative to design both connectivity recovery strategies and routing algorithms for s. All known solutions, which exploit relay devices such as stationary relay nodes (s) and mobile data collectors (s), can be classified into two categories. One is employing s only for the purpose of establishing a connected intersegment topology with stable communication paths between every pair of segments [5–9]. This category of work generally aims to minimize the number of s during the restoration process. The other one relies mainly on s repeatedly visiting each individual’s segments for data collection and aggregation with a few s involved [10–18]. However, all of these works assume that either the terrain of is flat or the number of relay devices is unlimited.

Given that these assumptions are not realistic in real scenarios, our goal in this paper is to develop an efficient connectivity restoration strategy that takes both realistic terrain influences and quantitative limitations of relay devices into consideration.

*Our Contribution*. This paper presents a hybrid recovery strategy based on random terrain in s, namely, , that establishes a biconnected intersegment topology in a disconnected network with a limited number of s and MDCs; meanwhile, the energy cost for data collection and aggregation is minimized. The accomplishes our goal in this paper as follows:(1)To quantify realistic terrain influences, the area of interest () is mapped into a grid of equal-sized cells. Each cell is associated with a weight that represents the corresponding terrain influence within. We calculate , the weight of each path , by accumulating the weight of each cell along , so that the weighted complete graph is constructed based on minimum weight paths between segments.(2)A path planning algorithm () is developed on to build a Hamilton cycle of minimum weight as the biconnectivity restoration tour for s. And is proportional to the cost for data collection and aggregation during the connectivity restoration.(3)According to different numbers of s, two different relay nodes deployment strategy, and , are devised to merge intersected paths of by carefully choosing candidate positions for s, so that is greatly reduced.

The rest of the paper is organized as follows. Related work is covered in Section 2. The notions and terminologies are introduced in Section 3. The problem description is described in Section 4. The algorithm is elaborated in Section 5. Section 6 gives the theoretical analysis on approximation radio and complexity of . And the validation results are presented in this section as well. We conclude this paper in Section 7.

#### 2. Related Work

There are two categories of approaches pursued for connectivity restoration [19]: the first category is to establish connectivity without terrain influences; the second one is to federate disconnected segments with consideration of terrain influences.

There are many excellent works regardless terrain influences during the connectivity restoration, which fall into the first category. Some of these works that employ s deployment only are listed as follows. Cheng et al. formulate placing the fewest s to connect segments as finding the Steiner minimum tree with minimum number of Steiner points and bounded edge length [5]. Lee and Younis propose grid based approaches, [6] and [7], both of which recursively deploy s until all segments are connected. In [20], recovery algorithms are proposed to minimize the deployment cost of sinks and relays and guarantee all sensors have two length-constrained paths to two sinks. Sitanayah et al. [8] find a minimal set of s which ensures length-bounded vertex-disjoint shortest paths to a sink for each sensor node. Lee et al. [9] focus on achieving a biconnected intercluster topology. Other works that employ s, s, and mobile nodes are listed as follows. In [10], Senel and Younis devise a convex hulk based recovery strategy -. It finds convex hulks of segments; then, each optimal tour for a convex hulk is assigned a to restore the connectivity. In [13], a least-disruptive algorithm is designed, which considers the impact of topology change on network performance through selecting candidate mobile nodes based on routing tables. In [14], a -hop neighboring information based algorithm is presented, which drives the backup mobile nodes to its destination to avoid intersensor collisions. In [15], a localized hybrid timer based cut-vertex node failure recovery approach is proposed, which adopts cascaded movement to relocate the mobile nodes so that the timely restoration is ensured. Joshi and Younis [21] establish balanced and optimized data collection and aggregation tours using the mobile nodes within the network. They first construct a minimum spanning tree then successively split it around the center into partitions such that the segments of each partition form a convex hulk. Eventually, all available s are assigned to partitions to complete the recovery process. In [16], Liao et al. aim at providing target coverage and network connectivity establishment through the minimum movement of mobile sensors. In [11], a delay-conscious recovery strategy, , was proposed to federate disjoint segments with a limited number of relay nodes. In [12], a convex hulk based recovery scheme is designed, which assigns s for intersegment federation and deploys s for intercluster connection. In [18], a distributed algorithm is designed to decompose the deployment area into its corresponding skeleton outline, along which mobile s are placed to finish connectivity restoration.

There are many excellent works with consideration of terrain influences during the connectivity restoration, which fall into the second category. Zhou et al. [22] propose an extended rapidly exploring random tree () based algorithm to initiate a path for a mobile node to reach the intended destination without crashing into any obstacles. Senturk and Akkaya [23] investigate how realistic terrain influences affect network connectivity recovery. Then, they design a terrain based restoration strategy [24] that considers different terrain types, such as forest, hill, swamp, and flat. ReBAT attempts to find the least cost paths between disjoint segments regardless of the subsequent data collection and aggregation. Truong et al. [17] propose a family of algorithms under the consideration of the impact of obstacles on mobility and communication, all of which collaborate to restore the connectivity with the least number of relay nodes and meanwhile minimize the mobility cost of agents. In [25], Mi et al. propose an obstacle-avoiding connectivity restoration strategy to avoid convex obstacles and intersensor collisions; however, they fail to consider realistic terrain influences on the process of connectivity restoration.

In this paper, we focus on establishing a biconnected intersegment topology in a disconnected network with a limited number of s and s and meanwhile minimize the energy cost for data collection and aggregation. It is worth to mention that establishing a biconnected intersegment topology, the quantitative limitation of relay devices, and minimizing the energy cost for data collection and aggregation are seldom considered all at pervious works unlike ours.

#### 3. Preliminary

Some notations used throughout this paper are given first; the important symbols with their definitions are collected in Notations.

*Definition 1. *A weighted complete graph is a complete graph of vertices with each edge associated with its weight, where and denote the set of vertices and edges in , while stands for the set of weights of edges. To be more specific, the weight of an edge is equal to ).

*Definition 2 (see [26]). *An Euler closed trail is a closed trail that visits every edge of graph exactly once. A graph that has an Euler closed trail is called an Euler graph.

*Definition 3 (see [26]). *A Hamilton cycle is a closed trail that visits every vertex of graph exactly once. A minimum weighted Hamilton cycle of graph is denoted by .

Figures 2 and 3 show the examples of a Euler closed trail and a Hamilton cycle , where