## 4 Performance Evaluation of I\(k\)-Acm  
In this part, information loss and energy saving trade-off is deeply investigated. Since the effectiveness of multicasting depends on the locations of sinks and distribution of sensor nodes, different experiments with different WSN topologies are performed. Simulations are done by program that we developed in java. This program generates synthetic data with five attributes which are all categorical. Each categoric attribute has five distinct attribute values. I\(k\)-ACM is implemented and synthetic data is \(k\)-anonymized. In experiments, WSNs with different topologies are simulated and energy ratio calculations are performed according to Equation 7. Running of experiments are performed in a laptop having 1.20 Ghz CPU and 2 GB RAM. First experiment investigates the effect of sink locations. The size of WSN field is set to \(500\)m\(\times 500\)m. Distance of each hop, \(R\), is taken as 10 m. There are two sinks in the field, \(sink1\) and \(sink2\). It is assumed that each sensor is uniformly distributed through the region. In every region having size of \(10\)m\(\times\)\(10\)m, there is one group head sensor node. All the sensors convey their readings to their group head nodes. Then, they anonymize data and relays it to the sinks. Each group head node calculates the cost of multipathing and multicasting for a given set of data, chooses the best method for data sending. The number of hops from sensor node to group head node and from group head node to sinks are calculated and they are taken into consideration in calculation of energy consumption. Energy consumption does not only depend on the number of hops; length of the messages are also important for the final results. Message lengths are taken into account during energy calculations. Assume that energy consumption of method named as \"multipath method\" is denoted as \(E_{multipath}\). Energy consumption of method that uses multicasting when appropriate is represented as \(E_{hybrid}\). Energy saving ratio, \(ES\), is computed as follows:  
\[ES=1-\frac{E_{hybrid}}{E_{multipath}} \tag{6}\]  
\[ES=1-\frac{\sum_{for\text{-}all\_G}min((h_{G,sink1}.l_{k1})+(h_{G,sink2}.l_{k2 }),((h_{G,M}+h_{M,sink1}+h_{M,sink2}).l_{IkACM}))}{\sum_{for\text{-}all\_G}(h_{ G,sink1}.l_{k1})+(h_{G,sink2}.l_{k2})} \tag{7}\]  
Values of \(k1\), \(k2\) are chosen as 3 and 6 respectively. Input records have five attributes each having distinct four attribute values. The range of information loss is computed as [0.0 2.0] in this experiment. If all group head nodes use multipath method, information loss for the data sent to \(sink1\) is found as 0.44 and data loss for \(sink2\) is 0.88. Total information loss of the whole system is 0.66 for multipath method. If multicasting with I\(k\)-ACM is used when appropriate, information loss for \(sink1\) also does not change since the first step of I\(k\)-ACM is a normal \(k1\)-anonymization step. However, information loss of \(sink2\) and energy saving ratios change. Table 4 gives the results obtained for different sink locations. Five different locations as given in the first column are chosen. Second column presents total information loss occurred in the system. The number of nodes using multicasting and multipathing methods are shown in third and fourth columns. Last column gives the result of energy saving according to the case when all nodes are using multipathing method. As the sinks get closer to each other, it is observed that the number of group head nodes using multicasting increase due to finding optimum multicast points. In the case where the sinks are located in coordinates of (0,0) and (500,500), sinks have the maximum distance between each other. 716 group head nodes, out of 2500 nodes, choose multicasting as the best alternative. Information loss increases to 0.73 bits but energy gain is very limited, 3%. In this topology, the number of multicasting nodes is lower and energy consumptions of hybrid and multipathing methods do not differ.