# A Matrix-Based Proactive Data Relay Algorithm for Large Distributed Sensor Networks
## 1 Introduction  
Large distributed sensor networks have been widely used in both military and civilian applications [1], such as target tracking [2], disaster response [3] and field surveillance [4]. In these applications, although each sensor is able to get some crude information, the data is usually imprecise or noisy with very low fidelity. As a consequence, the data in this form cannot be directly used for automatic planning or supporting human decisions, and has to be fused with other relevant data [5]. To fuse distributed data in a network, the key is to relay multiple-source data and aggregate enough amount of data to a single node in order to achieve high confidence information fusion [6]. However, with the progress of the development of state-of-the-art mobile sensor applications, networks emerge with new characteristics that pose challenges to existing information fusion approaches. The astronomical growth of networks involving thousands of sensors is a typical challenge in this respect. In these large networks, no single sensor can respond as the center and gain complete statistic of states of the entire network. In addition, because these networks are dynamically changing due to the mobility of sensors, or movements as a result of the surrounding air or ocean currents [7], nodefailures are not rare. Additionally, most sensors in these large networks have lightweight processing units, which make high constraint of energy consumption ideal for their operations. Following the importance of information fusion, many data relay protocols have been developed to diffuse data in sensor networks. Flooding [8] adopts a straightforward protocol for sensors to rebroadcast any new data received, but suffers from the intrinsic excessive energy consumption and network congestion due to the large number of duplicated messages. Traditional hierarchical [8] or centralized routing [9; 10; 11; 12] approaches, which are designed for fixed structure or where only sink nodes respond to information fusion are not also ideal for data fusion in mobile sensor networks. The predefined backbone nodes in these approaches will exhaust their power very quickly because of the heavy transmission burden and enormous cost on routing maintenance. To avoid these problems, many other distributed approaches have been developed for cases whereby all nodes can be treated as sink nodes. Those approaches include Information via Negotiation(SPIN) [13], Scalable Broadcast Algorithm (SBA) [14], The Lightweight and Efficient Network Wide Broadcast (LENWB) [15], Dominant Pruning [16] and Dynamic Probabilistic Flooding Algorithm [17]. Even though these approaches can guarantee a high quality information fusion, not all sensors would need all the data because any piece of information can only be fused by the sensor that aggregates enough relative data first. Therefore, the unnecessary data coverage may end with huge amount of energy consumption and redundant communication cost. SPIN can address this limitation to some extent by negotiating before broadcast, and allows sensors to transmit only data that others would need. Unfortunately, it is a reactive protocol, and a large number of negotiated messages makes it time-consuming and cost-ineffective for distributed data fusion. Some algorithms [18] can proactively relay data by forecasting the needs before a given set of data is broadcast. For example, a sensor would rather like to rebroadcast the data that is relative to the data of its neighbors only. However, when sensors cannot gain a complete view over an entire network, an intelligent proactive algorithm could be very difficult to implement [19]. In this paper, we present a novel matrix-based energy-saving and proactive algorithm to relay data in large distributed sensor networks. To deliver the core competence of this approach, we employ no querying process, and each node proactively forwards data to its neighbors by estimating the needs of neighbors based on its local knowledge about itself and the neighbors.