## 5 Experimental Results
The number of \"crossings\" is reported in the last four columns of Table 2.  
Note that variation of vectors \(\mathbf{v}_{i}(t)\) does not have to be uniform. Taking on account distribution of signals at each node may lead to additional communication savings. We illustrate this statement by a simple example involving just two nodes. If, for example, there is a reason to believe that  
\[2\|\mathbf{v}_{1}-\mathbf{v}_{1}(t_{i})\|\leq\|\mathbf{v}_{2}-\mathbf{v}_{2}( t_{i})\| \tag{15}\]  
then the number of node violations may be reduced by imposing node dependent constraints  
\[\|\mathbf{v}_{1}-\mathbf{v}_{1}(t_{i})\|<\delta_{1}=\frac{2}{3}\delta,\;\text {and}\;\|\mathbf{v}_{2}-\mathbf{v}_{2}(t_{i})\|<\delta_{2}=\frac{4}{3}\delta\]  
so that the faster varying signal at the second node enjoys larger \"freedom\" of change, while the inequality  
\[\left|\left|\frac{\mathbf{v}_{1}+\mathbf{v}_{2}}{2}-\frac{\mathbf{v}_{1}(t_{ i})+\mathbf{v}_{2}(t_{i})}{2}\right|\right|<\frac{\delta_{1}+\delta_{2}}{2}=\delta\]  
holds true. Assignments of \"weighted\" local constraints requires information provided by Equation (15). With no additional assumptions about signal distribution, this information is not available. Unlike [11] we refrain from making assumptions regarding possible underlying data distributions, instead we estimate the weights as follows:  
1. Start with the initial set of weights \[w_{1}=\ldots=w_{n}=1\;(\text{so that}\;\sum_{j=1}^{n}w_{j}=n)\] (16)
2. As texts arrive at the next time instance \(t_{i+1}\) each node computes \[W_{j}(t_{i+1})=W_{j}(t_{i})+\|\mathbf{v}_{j}(t_{i+1})-\mathbf{v}_{j}(t_{i})\|,\;\text{with}\;W_{j}(t_{0})=1,\;j=1,\ldots,n\] If at time \(t_{i}\) a local constraint is violated, then, in addition to \((d+2)|\mathbf{N}|\) messages (see Equation (14)), each node \(j\) broadcasts \(W_{j}(t_{i})\) to the root, the root computes \(W=\sum_{j=1}^{n}W_{j}(t_{i})\), and transmits the updated weights \[w_{j}=n\times\frac{W_{j}(t_{i})}{W}\;(\text{so that}\;\sum_{j=1}^{n}w_{j}=n)\] back to node \(j\). Broadcasts of weights cause increase of total number of messages per iteration to  
\[(d+4)|\mathbf{N}| \tag{17}\]With inequalities in Step 6 of Algorithm 4.1 substituted by \(\|\mathbf{v}_{j}-\mathbf{v}_{j}(t_{i})\|<\delta_{j}=w_{j}\delta\) the number of mean computations is reported in Figure 5:0  
It is of interest to compare results presented in Table 3 with those reported, for example, in [9]. The comparison, however, is not an easy task. While [9] reports the threshold \(r=0.0025\) as the threshold value that incurred the highest communication cost, the paper leaves the concept of \"communication cost\" undefined (we define transmission of a double precision real number as a single \"message\"). In addition [9] provides a graph of \"Messages _vs_. Threshold\" only. It appears that the maximal value of \"bosnia Messages _vs_. Threshold\" graph is somewhere between \(100,000\) and \(200,000\). We repeat the experiments with \"ipo\" and \"febru\" and report the results in Tables 4 and 5 respectively. The results obtained with stream dependent local constraints is a significant improvement over those presented in [10]. Consistent with the results in [10]\(l_{1}\) norm comes up as the norm that requires smallest number of mean updates in all reported experiments.