Elsevier

Computer Networks

Volume 57, Issue 4, 13 March 2013, Pages 1037-1047
Computer Networks

Topology control based on optimally rigid graph in wireless sensor networks

https://doi.org/10.1016/j.comnet.2012.12.002Get rights and content

Abstract

This paper presents an optimization scheme of sensor networks for node scheduling and topology control, aiming to reduce energy consumption for heterogeneous Wireless Sensor Networks (WSNs) with non-uniform transmission ranges. Motivated by geographical adaptive fidelity (GAF), we partition sensors into groups based on the location of sensors, such that a connected backbone network can be maintained by keeping only one arbitrary node from each group in active status while putting others to sleep. In addition, optimally rigid geographical adaptive fidelity (ORGAF) approach is proposed to decrease the communication complexity and reduce the energy dissipation. Furthermore, we prove the topology derived under ORGAF is 2-connected; and the average degree of nodes in the topology converges to four approximately. Simulation results show that ORGAF can improve the network performance as well as reducing the energy consumption.

Introduction

Advancements in the fields of Very Large Scale Integrated Circuits (VLSI) technology have greatly reduced the size and cost of electronic devices. The decreased size and cost lead to the development of multi-functional embedded sensor nodes. In wireless sensor networks, the energy source provided for a long working time without recharging. Moreover, since sensors are often intended to work in remote or hostile environments such as a battle field or desert, it is undesirable or impossible to recharge or replace the battery power of all the sensors. So it is critical to save energy in sensor operations. Two strategies are usually used to decrease energy dissipation in sensor communication.

The first strategy is based on topology control algorithm to adjust the radio transmission power of each node. Several topology control algorithms [1], [2], [3], [4], [5], [6], [7], [8], [9] have been proposed to create a power-efficient network topology in wireless sensor networks. COMPOW [1] and CLUSTERPOW [2] are approaches implemented in the network layer. Both hinge on the idea that if each node uses the smallest common power required to maintain network connectivity, the traffic carrying capacity of the whole network is maximized, the battery life is extended, and the MAC-level contention was mitigated [4]. In [5], Local minimum spanning tree (LMST) is proposed. Each node builds its local minimum spanning tree independently and only keeps on tree nodes. Localized Delaunay triangulation (LDel(k)) [6] is also a well-known topology control scheme, but it requires nodes to collect k-hop neighbors. An assumption that the nodes have detailed information about their neighbors is commonly made in the above algorithms. The authors in [7] proposed a practical topology control algorithm XTC, where nodes can conclude information about their neighbors merely based on their relative signal strength. The relations among the above structures were studied in some literatures [8], [9]. What is more, the authors in [9] presented a t-adjustable planar (TAP) structure which enables each node to adjust the topology independently via a parameter t and allows nodes to have different path loss exponents. However, most of these researches assumed homogeneous wireless nodes with uniform transmission ranges (except [4]). The assumption of homogeneous nodes does not always hold in practice since even the same type of devices may have slightly different transmission power.

The second strategy is scheduling sensor nodes to rotate between active and sleeping status. The sensor nodes must be activated in order to monitor the surveillance area. If all sensor nodes are activated at the same time, it may lead to redundancy in sensing, as the same area may be monitored by more than one node, and also there would be wastage of the precious energy resources. “To minimize the number of sensor nodes to be activated, while maintaining the coverage of the area” [10], which is the objective of coverage problem. The related researches include [4], [11], [12], [13], [14]. Span in [13] is a connectivity-maintained protocol that adaptively elects “coordinators” of all nodes in the network. It can close unnecessary nodes while it can maintain a well connected network and ensure that the nodes in sleeping status at least connect with one node in active status. Adaptive self-configuring sensor network topology (ASCENT) [14] is also a connectivity-maintained protocol. Span depends on the routing protocol while ASCENT can build data path without routing protocol. The property of robustness is one of metric evaluating the topology. A topology with robustness can cope with emergencies and has the ability of adaptation to the unpredictable environment. GAF [11] partitions the nodes based on their geographic locations. It divides the deployed area into multiple equal size squared virtual grids so that nodes in the same cell form a group. By choosing the appropriate side length of virtual grid, it ensures that a well robust network can be formed as long as at least one node in each virtual grid remains in active mode. The active node in each virtual grid cost more energy because of undertaking the more tasks, so we should choose the node with more remaining energy as the active node. Considering the mentioned above, Santi et al. in [15] proposed an improved algorithm, two schemes of choosing the active node are designed. In [16], the authors put forward a scheme to solve the problem that some cells may have no node, which destroys the connectivity of the network. But GAF also depends on the assumption of homogeneous wireless nodes with uniform transmission ranges as most of algorithms. GAF actually provides a 4-connected or well robust backbone network for a large sensor network. However, the topology derived under GAF is with higher node degree (see Fig. 6a after the text), besides the problem discussed above. Node degree is the number of neighboring nodes communicating directly in wireless sensor networks. The high degree of nodes means severe interference and conflict between the transmitted signals, packets may need to be transmission repeatedly and consume a large amount of unnecessary energy. From the above discussion, the robustness and the simplicity of the topology are of the same importance. Therefore, an algorithm which constructs a topology with the capability of maintaining a reasonable node degree while keeping the robustness is desired.

In this paper, we propose a decentralized algorithm combined sleep scheduling with topology control, called ORGAF. The work aims to decrease the link among active nodes to reduce the energy dissipation, while preserving the connectivity of the network. Rigid graph and optimally rigid graph are introduced as the main part of proposed algorithm. ORGAF partitions the nodes based on their geographic locations as the same as GAF and at least one node in each virtual grid remains in active mode. The contributions of this paper include: (i) the topology generated by ORGAF is 2-connected; (ii) the average degree of nodes in the topology converges to four approximately. Feature (i) reflects the robustness of the topology constructed under ORGAF, a topology with robustness can cope with emergencies and has the ability of adaptation to the unpredictable environment. Besides, Feature (i) is critical for packet transmissions reliably. Feature (ii) reduces the negative impact of other factors, such as node density, on the finally optimized topology and entitles the topology from ORGAF with certain independence and predictability; meanwhile, the predictable average degree provides a reference basis to the distribution of network limited resources in practical applications. In simulation process, ORGAF has a better performance in balancing traffic loads among the network nodes.

The rest of this paper is organized as follows. Section 2 give the network model and introduce some important notions. Section 3 describe the proposed distribute algorithm. To verify the validity of algorithm, simulation results are given in Section 4. Finally, conclusions are made in Section 5.

Section snippets

Network model

In this work, we make some simple, common and realistic assumptions firstly. They are catalogued below.

  • 1.

    Monitoring area is big enough relative to the communication range, and boundary factors can be ignored.

  • 2.

    The sensor nodes are aware of their location coordinates.

  • 3.

    The sensing range of a sensor node is assumed as perfect disks, which means, the sensing range of a node is r > 0, the node can sense the target, if it is within a distance of r from the node.

  • 4.

    The communication range of a sensor node Rc is

Algorithm description

In this section, we describe the proposed algorithm ORGAF. To reduce the energy consumption of communication in sensor networks, GAF [8] divides sensor nodes into several groups based on their geographic locations such that only one node in each group keeps active at each snapshot while others are put into sleeping. In Section 3.1, we adjust (decrease) the side length of “virtual grid” to keep the topology connected even in heterogeneous WSNs. However, decreasing the side length of “virtual

Performance evaluation

In this section, we provide some simulations results in Matlab R2007a. to analyze the performance of the implemented algorithm. In all the simulations, we consider the side length of “virtual grid” as a constant r = 1 for convenience and the maximum transmission range Rm can be chosen an arbitrary value larger than 8/(1-DOI) in the light of Lemma 5. DOI is set to be 0.1, and the transmission range Ri of an arbitrary node i is within between (1  DOI)Rm and Rm. We run the distributed algorithm ORGAF

Conclusions

In this paper, we propose a decentralized algorithm combining sleep scheduling with topology control. The work aims to decrease the link among active nodes to reduce the energy dissipation, while preserving the connectivity of the network. We partition sensors into groups based on the geographic location information of sensors, such that a connected backbone network can be maintained by keeping only one arbitrary node from each group in active status while putting others to sleep. And optimally

Acknowledgements

This work is supported by the National Basic Research Program of China (973 Program) (2010CB731800), the National Natural Science Foundation of China (60974018 and 61074065) and the Natural Science Foundation of Hebei Province (F2012203119).

Luo Xiaoyuan received his Ph.D degree in Control Theory and Control Engineering from Yanshan University, China, in 2005. He is currently a professor of the Institute of Electrical Engineering, Yanshan University. His current research interests include topology optimization and cooperative control for multi-agent systems, netwoked control systems.

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    Luo Xiaoyuan received his Ph.D degree in Control Theory and Control Engineering from Yanshan University, China, in 2005. He is currently a professor of the Institute of Electrical Engineering, Yanshan University. His current research interests include topology optimization and cooperative control for multi-agent systems, netwoked control systems.

    Yan Yanlin received her BS degree in communication engineeringand from Yanshan University, China, in 2009. Now she is a candidate for MS in control science and engineering at Yanshan University, Hebei Province, China. Her research interest is topology optimization and cooperative control for multi-agent systems.

    Li Shaobao received his BS degree in automation and MS degree in control science and engineering from Yanshan University, China, in 2006 and 2011, respectively. He is continuing his position as a Ph.D student at City University of Hong Kong. His current research interests include cooperative control for multi-agent systems and wireless sensor networks.

    Guan Xinping received MS degree in Applied Mathematics from Harbin Institute of Technology, Heilongjiang Province, in 1991, and Ph.D degree in Electrical Engineering from Harbin Institute of Technology, China, in 1999. He is currently a professor of Shanghai Jiao Tong University, Shanghai, China. His current research interests include robust congestion control in communication networks, wireless networks and networked control systems.

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