## 1 Introduction  
In wireless sensor networks (WSNs) [1], a sensor network is composed of a large number of wireless sensors, densely deployed, in the range of a phenomenon to observe, study and monitor it. A sensor is an electronic device which generally combines three main capabilities: the ability to measure and collect data relative to the environment surrounding it, the ability to process these collected data, and the ability to exchange it with other devices. The other devices can be sensor nodes or sinks. A sink is a particular node, generally with no energy limitation, which collects the information resulting from the sensing nodes, processes it and/or sends it to a data concentration center.  
In a WSN cluster protocol, the network is randomly divided into several clusters, where each cluster is managed by a cluster head (CH). The sensor nodes transmit data to their cluster heads, which transmit the aggregated data to the base station. Localized clustering can contribute to more scalable behavior as the number of nodes increases, providing improved robustness, and more efficient resource utilization for many distributed sensor coordination tasks [2]. Data aggregation becomes more simple under cluster conditions. Many clustering algorithms exist in the literature (k-means clustering [3], self-organizing maps [4], LEACH (LEACH-c) [5], TEEN [6], PEGASIS [7], _etc._).  
As a novel issue, WSNs with multiple sinks have become a hot research topic. Many research works have focused on how to deploy sink nodes at optimal locations so the networks can cover relatively larger distances [8,9]. Even many mobile sink schemes were proposed [10] in wireless self-organized networks. This suggests that information about each mobile sink's location be continuously propagated through the sensor field to keep all sensor nodes updated with the direction for forwarding future data reports. Unfortunately frequent location updates from multiple sinks can lead to both excessive drain of sensors' limited battery power supply and increased collisions in wireless transmissions. Sink mobility brings new challenges to large-scale sensor networking [11]. In our opinion, it is more practical to improve the network's topology after the sink nodes are deployed by using a routing protocol and power control scheme.  
In this paper, we combine the multiple sink and cluster based routing technology. The MSCWSNs-PC is targeted at multiple sink clustering-based WSNs and is the first power allocation protocol developed for these networks, to our knowledge. The multiple sink cluster WSNs (MSCWSNs) can be simply divided into sink as cluster head and non-sink as cluster head mode. A topology illustration of multiple sink clusters is given in Figure 1. Both types of sink nodes need to negotiate the broadcast radius in order to obtain satisfactory network connectivity and decrease the mutual communication interference.  
This paper features the following major contributions:  
* It provides a distributed transmission power control algorithm for sink nodes in multiple sink WSNs.
* By using our algorithm, less sensor nodes needs to decide which sink should act as center of local subnetworks.
* The algorithm provides a high network connectivity.
* It is targeted at multiple sink cluster-based wireless sensor networks and is the first protocol developed for these networks, to our knowledge.  
In order to design good distributed power allocation protocols for multiple sink wireless microsensor networks, it is important to understand the parameters that are relevant to the sensor applications. While there are many ways in which the properties of a sensor network protocol can be evaluated, we use the following metrics: