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Broadcasting is a common and basic operation used to support various network protocols in wireless networks. To achieve energy-efficient broadcasting is especially important for

Recent advances in micro-electro-mechanical systems, digital electronics and wireless communications have led to the emergence of

In

To provide an efficient solution for the broadcast problem with consideration of energy consumption is an important issue in wireless sensor networks. As mentioned, sensor nodes are generally supported with limited energy budget, and energy efficiency is an important issue in wireless sensor networks. Radio is a main source of energy consumption in wireless sensor networks, which is generally comprised with three parts, namely, transmission power, reception power and idle power, and the idle power is small enough to be ignored compared with the other two [

An efficient way to build a spanning tree with a minimum number of non-leaf nodes is using the minimum Connected Dominating Set (CDS) for a given a connected network graph. Nodes in minimum CDS shall be connected and have to relay the received message, while other nodes shall have at least one neighbor located in the CDS. In this work, we have introduced an efficient heuristic algorithm to build the Minimum CDS (EMCDS). The basic idea is that we first select the Maximal Independent Set (MIS) with the help of a proposed ordered sequence list; then we build the connected dominating set by adding connected nodes into MIS; and finally we further optimize the result by removing some redundant non-leaf nodes.

The proposed EMCDS algorithm aims at providing a broadcast tree with minimum energy consumption for one single broadcast operation. However, because non-leaf nodes consume more energy compared with leaf nodes, the non-leaf nodes might become energy depleted in the broadcast operation goes on for a long time. This might result in single-node failures or network partition problems in case that the reserved energy cannot support the required operation. Sensor nodes can be carefully scheduled to balance energy consumption during the broadcast process. In this work, we have introduced a Minimum Energy-consumption Broadcast Scheme (MEBS) to avoid the node failure problem and aimed at providing an efficient scheduling scheme with the network lifetime maximized. The proposed algorithm uses a modification version of EMCDS with energy considered, and selects different relay nodes in a dynamic manner to improve the network lifetime.

The rest of this paper is organized as follows: in Section 2 we summarize related works. Section 3 describes our EMCDS algorithm and Section 4 concerns the proposed MEBS algorithm. Experimental results are presented in Section 5, while conclusions are drawn in Section 6.

The minimum-energy broadcast problem in wireless sensor networks has received significant attention over the last few years. Here, we will introduce the key mechanisms and characteristics of the broadcast algorithms that are among the most representative of this research area.

Flooding is the simplest and most basic method for broadcast operation, but can lead to the known broadcast storm problem [

In many works, the broadcast problem is converted to the problem of finding a spanning tree. One notable contribution was the Broadcast Incremental Power (BIP) algorithm proposed by Wieselthier

Sausen

Papageorgiou

Several schemes based on distance were proposed for broadcasting. DB (distance based) was one of the schemes used to minimize the effects of the broadcast storm problem when disseminating information in wireless networks [

Network coding can be used by the intermediate nodes to combine packets before forwarding. Therefore, it can be used for broadcasting to reduce the total number of transmissions. Li

In order to find better solution, some mathematic heuristic approaches were put forwarded for the MEB problem. Das

Considering the minimum-energy broadcast problem can be stated as a combinatorial optimization problem, some scholars used swarm intelligence algorithms to solve the minimum-energy broadcast problem. Wu

Lou

The known connected dominating sets (CDS) can be used to solve the minimum-energy broadcast problem in wireless sensor networks. In [

In this section, we introduce a novel EMCDS algorithm to find the minimum CDS for a given connected graph. The process of the proposed algorithm can be divided into two main steps: (1) Construct an ordered sequence list for all nodes in the network with the help of breadth first algorithm, and build MIS with the ordered sequence list; (2) Connect the above MIS by adding some connected nodes and build CDS, then optimize the connected dominating set and obtain the minimum CDS. The symbols used in the algorithm and details for these steps are described as follows.

The wireless sensor network can be modeled as an undirected graph

Let

Let

MIS is the infrastructure while building MCDS. There are already many methods to build the MIS. In this work, we have introduced a novel notation named

Input: the wireless sensor network

_{i}

As we can see from the pseudo code, Lines

In this algorithm, we use different state values to mark the roles of nodes in the network. The nodes are initialized as

Nodes in the MIS shall be connected to provide a solution for the broadcast problem. Here we introduce an EMCDS algorithm in which we firstly build a CDS and then minimize its size by removing some nodes. The pseudo code of the EMCDS construction is described as follows (Algorithm 2):

Input: the wireless sensor network

_{i}

_{i}

_{i}

_{j}

_{i}

_{k}

_{i}

_{i}

Lines _{1} = {2}, _{2} = {3}, _{3} = {4, 5}, _{4} = {6} accordingly.

However, with the same example there is still redundancy with the above CDS construction process. For example, node 6 can be removed from the dominating set because it has no children. In the algorithm, we introduce steps to remove such redundant nodes via Lines

Here we introduce a simple example to demonstrate the process of the proposed EMCDS algorithm. The network is composed with 12 sensor nodes deployed in 10 m × 10 m area.

The next step in MISC algorithm is to build the required MIS. Initially, all nodes are marked as

Then we check the status of nodes in Layer 2. The node with highest prior in Layer 2 is node 6, which is then marked as _{6} = {10, 11}. Then next node 7 is selected, and the similar steps carried out, and finally node 7 is marked as _{7} = {12}. Similarly, in the next step, node 5 and 8 are selected ad marked as _{5} = {9}, _{8} = Φ. Now we check nodes in Layer 3 and find that they are all covered, and so node 9, 10, 11, 12 are marked as

Then we shall add nodes into _{2} = {1, 3}, _{3} = {1, 2, 4}, _{4} = {1, 3}, _{5} = {2}, _{6} = {3, 2}, _{7} = {3, 4}, _{8} = {4}, _{9} = {5, 10}, _{10} = {6, 5, 9}, _{11} = {6, 7, 12}, _{12} = {7, 11}. Secondly, node 1 is marked as _{6} are not included in _{6}, _{3} = {6}. Thirdly, node 3 is the first node in _{7} and is already included in _{3} = {6, 7}. Since that node 5 has only one candidate parent as node 2, node 5 is marked as _{2} = {5}. In the same way, node 8 is marked as _{4} = {8}. Finally, all nodes are marked

In the following we illustrate how to use the proposed steps in EMCDS algorithm to remove the redundant nodes from _{6} = {10, 11}, and node 10 can choose node 5, node 11 can choose 7 as their parents. Accordingly, node 6 is removed from _{5} = {9, 10}, _{7} = {12, 11}, _{6} = Φ. We check all nodes in

Theorem 1. The time complexity for the EMCDS algorithm is ^{3}).

Proof. We analyze the complexity for each step in the EMCDS algorithm. (1) the time complexity for the breadth-first-search algorithm is ^{2}); Finally we traverse all nodes in CDS and their parents to remove the redundant nodes, and it is ^{3}). In this way, the total time complexity of the EMCDS algorithm is ^{2}) + ^{3}) = ^{3}).

The previous proposed EMCDS algorithm can solve the minimum-energy broadcast problem in wireless sensor networks, in which nodes in MCDS will forward the received messages while nodes excluded in MCDS only need to receive message from their parent nodes. By reducing the number of nodes in MCDS, the algorithm helps to minimize the total energy consumption during the broadcast operation. However, the relay nodes will consume more energy compared with the leaf nodes, and such uneven energy consumption might lead to node failure or network partition. In this section, we first modify the proposed EMCDS algorithm with consideration of the balance of the energy consumption, and then we introduce a new MEBS algorithm to schedule the sensor in sequence for the broadcast operation and aim at providing a scheme with the network lifetime maximized.

The energy efficiency of the broadcast operation concerns severely with the model for energy consumption in the ad hoc sensor networks. Nodes have an initial energy and its value is denoted as

Note that in the previous section, the proposed EMCDS algorithm is concerned with finding a CDS with a minimum number of nodes. The balance on the energy consumption shall be further considered to avoid the node failure or network partition problem. We introduce the modification on the previous EMCDS algorithm as follows.

Nodes cannot act as non-leaf nodes if their reserved energy is less than

Remove the nodes with reserved energy less than

If it is the first time to construct the broadcast tree, order all nodes in decreasing order of the node degree; otherwise, order them in random sequence; and the final result is preserved in list

For each node _{i}

Similarly, Nodes cannot act as the connected nodes if their reserved energy is less than

If node _{i}_{i}_{j}_{i}_{k}

The basic idea behind the MEBS algorithm is that we re-construct the broadcast tree if it is necessary. We consider the two special conditions that the broadcast tree is built again as: (1) nodes in the MCDS have spent too much energy on broadcast operation and their total energy runs to a critical point; (2) The reserved energy of the relay node cannot support any forwarding operation. For the first situation we adopt a new parameter

Input: Network

In this section, we give experimental results for our proposed EMCDS and MEBS algorithms and comparisons with related works. We also analyze the impact of parameters on MEBS. The simulation is done on the Matlab platform.

In this section, we study the performance of our designed EMCDS algorithm compared with other works by experiments. Wireless sensor networks are built with various numbers of nodes and transmission ranges in a 100 m × 100 m square area. When the node position and the transmission range are given, there is an edge between two nodes if their distance is no larger than the transmission range, and then the network

For the first scenario, a certain number of nodes (first 200 nodes and then 1,000 nodes) are uniformly distributed in a plane. The transmission range

For the second scenario, a certain number of nodes ranging from 100 to 600 are uniformly distributed in a plane. The transmission range

The MEBS algorithm aims at providing a scheduling scheme with the maximized network lifetime. There are a variety of metrics can be used to measure the performance of broadcast protocols, as mentioned in the related works. However, a commonly used metric is the number of message re-transmissions with respect to the number of node in the network. In this work, we use the

The results for

In the following, we will compare the network lifetime via different scheduling algorithms. However, Liao [

The proposed MEBS will re-construct the broadcast tree according to the parameter

Based above observation, we can see that the

Energy-efficiency is a criterion for sensor nodes and how to perform energy-efficient broadcasting is an important issue in

In future work, we plan to develop a distributed version of the proposed EMCDS and MEBS algorithms for energy-efficient broadcast problems. Wireless sensor networks are expected to be used in various applications because not only are the sensor nodes rather cheap, but also their robustness and

This work is supported by Fujian Provincial Natural Science Foundation of China under Grant No. 2011J01345, the Development Foundation of Educational Committee of Fujian Province under Grand No. 2012JA12027, National Natural Science Foundation of China under Grant No. 61162009, and the Technology Innovation Platform Project of Fujian Province under Grant No. 2009J1007.

An example network with six nodes.

Network topology of the given example.

Layers for the given example.

MIS construction for the given example.

CDS construction for the given example in EMCDS algorithm.

Remove redundant nodes in the EMCDS algorithm.

The size of MCDS with different transmission range. (

The size of MCDS with different number of nodes. (

Saved rebroadcast with different transmission range.

Saved rebroadcast with different number of nodes.

Network lifetime with different transmission range. (

Network lifetime with different number of nodes. (

The impact of threshold on the performance of MEBS. (

The impact of threshold on the performance of MEBS. (

Notation of the Symbols.

Sink/source node | |

Network size | |

Layer list for nodes according to their distance to the source | |

Variable used to denote the distance/layer to the source | |

Transmission range of the sensor nodes | |

Ordered sequence list | |

_{i} |
The list of children for node |

_{i} |
The list of candidate Parents for node |

The set for the Maximal independent set | |

The set for the connected Dominating set |

Coordinates for nodes in the example.

ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Axis | ||||||||||||

5 | 3 | 5 | 7 | 1 | 4 | 7 | 9 | 1 | 2 | 6 | 8 | |

8 | 7 | 6 | 7 | 6 | 5 | 4 | 9 | 3 | 4 | 3 | 2 |