The fundamental goal of a sensor network is to produce, over an extended period of time, globally meaningful information from raw local data obtained by individual sensor nodes. Importantly, this goal must be achieved in the context of prolonging as much as possible the useful lifetime of the network and ensuring that the network remains highly available and continues to provide accurate information in the face of security attacks and hardware failure [11]. WSNs experienced a great expansion these latest years. In fact, many works had been done in this domain; especially in the data routing and more precisely in permutation routing in a multi-hop environment. Bomgni et al. in [8] have introduced a deterministic routing protocol for permutation routing in dense multi-hop sensor networks, which is realized in broadcast rounds in the worst case. Lakhlef et al. proposed in [7] an improvement of the previous protocol that runs in broadcast rounds. Where n is the number of items stored in the network, p is the number of sensors, is the number of sensors in the clique of maximum size and k is the number of cliques after the first clustering. However, the protocols presented in [8] and [9] assume that all network stations are awake during the entire execution of the protocols.

Heinzelman et al. [12] introduced a hierarchical clustering algorithm for sensor networks, called Low Energy Adaptative Clustering Hierarchy (LEACH). LEACH is a cluster-based protocol, which includes distributed cluster formation and rotation of the CH’s role while transmitting data. An enhancement over LEACH protocol called PEGASIS (Power-Efficient Gathering in Sensor Information Systems) was proposed by Lindsey et al. in [13]. PEGASIS is a near optimal chain-based protocol in which, each node communicates only with a close neighbor and takes turns transmitting to the base station, thus, reducing the amount of energy spent per round. The protocols presented in [12] and [13] assume that the memory capacity of the sensor nodes is not limited.

We consider a WSN of p stations which contains n items, each station has initially items. We propose an energy efficient hierarchical permutation routing protocol which performs in 4 stages. The first stage is devoted to the clustering of the network into disjoint cliques where a CH is elected [4]. The second stage is the transformation of cliques obtained after the previous stage in a hierarchy of cliques using [10]. The third stage is allocated to the routing of external items toward their directed clique. Finally, in each clique, we route the internal items to their destination. We show that according to certain parameters, each station has a memory complexity of

The remainder of this paper is organized as follow: in Section 2, we present the new hierarchical permutation routing protocol for WSNs. Section 3 deals with some experimental results. A conclusion with open problems ends the paper (Section 4).

In order to properly run this protocol, it is important to define certain bases. At first, consider that the network has p stations, each of them stores items and has a unique between 1 and p. Again, we consider that k channels of communication are available to allow the sensors to communicate. Hence, we write and we read wireless sensor network with p stations and k channels. We suppose that n items circulate in the network. Each of the p stations has items. Each item is a pair . Where is the data to be send to sensor v. Item held by a station may or may not have itself as destination station. Figure 1 illustrates an example of permutation routing in a WSN of 9 stations.

Clustering has become a prominent approach to reduce energy consumption in WSNs [14]. In clustering, the network is arranged in clusters of nodes, where each cluster (clique) consists of member sensors, gateways, and a cluster head. The main objective in this first stage is to partition the set of sensors of the network in cliques. Note that clustering can be done in two ways: first, the Node-Centric method consists of choosing the cluster head before choosing clique member’s, and the second method, Cluster-Centric, does the reverse of the first method [8] [15]-[20]. We use the second approach to partition the network in our protocol. Indeed, we will use the protocol presented by Sun et al. in [4] to partition our network. At the end of this, we obtain a number of disjoint cliques within which stations are interconnected to each other, i.e. communication within each clique is one-hop, and each station knows the other’s identity. After clustering, the members of different cliques are responsible for electing the CH. Thiselectionisdone as follows:

1. Each node broadcasts its residual energy with its member’s clique. The sensor with the higher residual energy is then elected as CH.

2. If each of them has the same residual energy, the CH is the one that has the higher ID.

3. After sending items of a particular clique, the station whose identifier is directly below that of the current CH becomes the new CH. If the current CH has the smallest ID, the station with the greater ID will be the new CH. This is doing so on, until all cliques received their destined data.

Figure 2 shows in (a) a network of 10 not-partitioned sensors and (b) the same partitioned network into cliques (3 cliques) using the protocol presented by Sun et al. At the end of this step, all the external items of each clique are known.

At the end of the previous stage, we obtained a set of k cliques (so k CHs). Our goal now is to constitute a hierarchical structure to ensure efficient data routing. For this, we use the protocol presented by Banerjee et al. in [10] . Indeed, the realization of that protocol is made as follows: starting from an initial set of sensors, a multi level covering tree cluster is constructed reassuring that each clique has a number of nodes between x and 2x, where x is an integer value parameter. To apply this, we use the k CHs obtained after the first stage. We set

and we obtain a single cluster [10] . It should be noted that the obtained superclusterhead after the hie-

rarchical clustering knows the identity of all members of the cluster (which actually are the others CHs obtained after the first stage).Figure 3 illustrates a hierarchical clustering (1, 2, 3, 4, 5) with a parameter given,

using the protocol of Banerjee et al. [10] .

After this stage, the cliques are in a well-defined hierarchy where it remains only to establish the order to transfer data to external cliques.

As in the protocols presented in [8] and [9] , the communication among clusters is made using gateways. In other words, when a station within a clique has the item destined to a particular station in another clique, it sends the item from gateway to gateway until it reaches the gateway of the destination clique. At this time, the latest gateway is charged to send the item at the final destination. Figure 4 illustrates this principle. Moreover, a communication channel is assigned to each clique.

To make it simple, we consider that if x is the number of available channels and k the number of cliques obtained from stage 2, then . Let’s remember that at the end of stage 2, we get a tree that all nodes are CHs and leaves are sensors where one of the CHs is the CH of the tree (superclusterhead).

The pseudo-code of our protocol is as follows (see Figure 5).

Let p sensors in a multi-hop sensor network with n items pretitled on it. Without clustering broadcast slots, the permutation routing problem can be solved in time slot in the worst case with no station being awake for more than slots where.

Proof: By summing the results of both lemmas, the time required for internal routing in each clique and the time required for the general scheduling of the cliques, we obtain the result. Indeed, and.

Proof: The proof of this theorem is made as follows:

1) Before the running of the protocol, it is assume that each station has in his internal memory a total of.

2) During the protocol process, the worst case occur when on the path from the super clique to the clique of maximum number of stations, items have to pass throw the clique of minimum number of stations. The total number of items destinate to clique is. Thus, each station of the clique must store items. According to our hypothesis, we obtain. Hence, it is concluded that the memory allocated for routing items in different stations is at most.

The energetic model we use is similar to the one in [13],

where and are respectively the energy used for the transmissions and the receptions of items in the network. The energy dissipated by the transmitter, the amplifier and the receiver are respectively expressed by and . Moreover, d is the Euclidian distance between nodes, N is the energy parameter mitigation ( ) and n represents the number of items. Thus, based on this model, we value to and to with initial energy of sensors to and then, we have the Figure 6. This figure is the one which represents communication between two nodes. The curve's energy dissipate while transmitting items to that of the items sender, and the curve of the energy waste while receiving items is that of the receiver node.

Figure 7 represents the evolution of the average number of cliques based on the number of nodes of the network. We randomly generate a graph with the labels on the nodes. Then, we partition the previous graph using the protocol of Sun et al. [4] and therefore we get the number of cliques.

In the Table 1, we did a comparative study of our protocol to those presented by Bomgni et al. [8] and by Lakhlef et al. [9]. From this table, it is clear that the awaking time taken by our protocol is less than that presented in [8] and [9]. For instance, for and , the sensors stay awake during 18203881 slots in our protocol, while in the protocols of Bomgni et al. and Lakhlef et al., the sensors stay awake during 19006435 and 46454931 slots respectively. In addition to the awaking time which is better for our protocol, on can noted that

our protocol is executed in consideration of the different memory sizes of sensors’ network that is about,

in contrast to those presented in [8] and [9] where the memory size of the sensors are infinite.