Distributed Broadcast Minimum Spanning Tree (reliable version) Ahmad Kardan 1 , #Mohammad Kajbaf 2 1 Computer Engineering Dept., Amirkabir University of Technology 2 Azad University of Masjid-Soleyman kajbaf@aut.ac.ir Abstract DBMST is a broadcast communication protocol that provides a distributed MST algorithm. It is based on the FPS power- management protocol. This paper presents the complete version of DBMST that regards packet loss and dynamism of the network topology and provides reliable communication. The proposed method decreases the power consumption of reliable broadcasting up to 15% in comparison with the basic version. In DBMST, network structure adapts to topology variations quickly, while it takes several hours for other methods to find out variations in network. 1. INTRODUCTION Due to the advances in MEMS micro-sensors, wireless networking and embedded processing, ad-hoc networks of sensors are becoming increasingly available for commercial applications such as environmental monitoring, monitoring critical infrastructures, and collecting data for battlefield awareness. One of the significant goals in such networks is to decrease power consumption. It is shown that no algorithm can generate a minimum spanning tree in a polynomial time, therefore heuristic algorithms are usually used to create MST paths[1]. In this paper, we study some MST algorithms for ad-hoc networks and FPS. FPS is a distributed on-demand power-management protocol for data acquisitioning in sensor networks [2]. Our method was described as BEFPS in [3]. In [4], two more extensions were applied. First, supporting multicast communications, and second, adaptation against variations in the environment. Here, two new extensions are added. First, supporting reliable communication; second, ability to reconstruct the network in the case of partial failure. DBMST is proposed for WSNs of low traffic rates that is the case in some environment monitoring applications. 2. TRANSMISSION POWER ESTIMATION Embedded systems manage the power consumption of different parts to decrease the overall power consumption. Nodes turn the radio module ON or OFF to manage the power consumption. Some systems also adjust the transmission power. This paper assumes that the nodes adjust their transmission power continuously, not discretely. A. Power Management Sensor nodes have to keep their radio ON even in idle times, waiting for possibly arriving packets. Therefore, a node consumes most of the energy for listening, although there is no packet to receive [2]. To turn the nodes off, the communication between nodes must be synchronized. If we consider the electric current as a measure of consumed power in radio, it is observed that the sensor nodes transmit data in some small period of time; then they get idle [5]. In DutyCycling power management scheme, all nodes wake up at the same time for a fixed waking period every EPOCH [6]. During the waking period, nodes exchange messages and take sensor readings. Outside the waking period, the processor, radio, and sensors are powered down. All nodes wake up every EPOCH for T seconds and exchange messages. Thus, the duty cycle is   ∗ 3600 seconds/hour. ‘FPS’ protocol, that is the underlying communication protocol of DBMST, uses a local scheduling method to synchronize communications between nodes. Time is divided to time- cycles, while each cycle is divided to time-slots. Nodes use advertisement messages to announce the free communication slots to the other nodes. In this way, each node knows when it should send a packet and when listen to the media. In idle times, radio or the node is turned off. Equation (1) expresses how to estimate power consumption of nodes. (mA.h) = radio_ON_time × ON_draw radio_OFF_time OFF_draw Power + · (1) B. Distance in Wireless Communications Intensity of electromagnetic wave is inversely proportional to the square of distance from its source, where there is no obstacle and the wave propagates in all directions. If directive antenna is used, source node is far away, or there are obstacles in the direction of the wave, the attenuation factor increases. According to [7], the intensity of transmitted beam degrades by the scale of 1/  in which r denotes the distance from the source of the beam, and a is the attenuation factor and 2 ≤ a <4. Suppose in an environment a is two, and there are two paths from node i to node j, a straight link and a two-hop path from node k. In the first case and second case, the consumed power is obtained from (2) and from (3), respectively. 0 ij ij e er a = (2) 0 ( ) ij ik kj ik kj e e e e r r a a ¢= + = + (3) 1