## 7 Conclusions and Future Work  
In this work, we have extended the results obtained by the MIP model previously presented thanks to a GRASP meta-heuristic capable of handling larger networks in terms of nodes and also larger tests in terms of number of critical nodes. Moreover, the decision of simultaneously removing such critical nodes instead of doing it iteratively has driven us to the following conclusions:  
* The simultaneous removal allows for covering the worst possible scenario, in which part of the network unexpectedly shuts down and many critical nodes are disabled at the same time. An IoT system distributed across many buildings or zones can have part of the network disabled due to natural disasters, malicious attacks or power outages. On the contrary, individual sensor incapacity is less likely to happen due to the possibility to monitor and prevent unwanted battery levels or sensor behaviors prior to the actual failure.
* In many cases, the iterative and simultaneous cases end up identifying the same nodes as critical. This means that if, for any reason such as time limitation or computational power, it is not possible to cover the simultaneous case, by computing the iterative scenario, it is enough to identify the most disruptive nodes with sufficient certainty. However, this should not be the common proceeding.  
Nonetheless, by looking at the results presented, we can appreciate that the identification of critical nodes is crucial to deliver good service even when the network is being disrupted. Although their impact on fixed deployment areas decreases as the number of nodes increases, their failure is still relevant enough to consider securing their integrity. Moreover, as deployment area scales, the impact of the critical nodes remains almost equal, contradicting the idea that, since there are more nodes, their importance should be lower as the number of nodes increases. Because of that, it is clear that the  
Figure 6: Average and maximum lifetime decrease values and execution times for networks with nodes distributed according to area specified in Table 6.  
security and reliability of the most influential nodes is very important to avoid the shut-down of a whole system network, which can induce large economic losses for a company that deeply relies on gathered data to acquire benefits or perform its duty correctly.  
Additionally, even though the meta-heuristics do not deliver an exact and correct result all the times, the success rate obtained offers a good opportunity for large scale scenarios in which exact optimization tools are unable to handle such amount of data.  
The individual contributions of the authors are as follows. [PERSON] investigated and conceptualized the problem, and created the formal analysis and the software needed to obtain and compare the results. [PERSON] validated the comparison between the GRASP and the ILP. [PERSON] and [PERSON], in addition to coordinating the work, they proposed to simplify the problem using a selected number of network features and the use of a GRASP algorithm. The draft was created by [PERSON] and revised by [PERSON] and [PERSON].  
This work has been partially funded by the Spanish Ministry of Economy and Competitiveness under contract FEDER TEC2017-90034-C2-1-R (ALLIANCE project) and supported but not funded by the Generalitat de Catalunya under contract 2017 SGR-1037.  
The authors would like to thank the editor and anonymous referees for their upcoming helpful comments in improving the quality of this paper.  
The authors declare no conflict of interest.