A power domination set in a network is a subset of its nodes such that by applying a simple set of rules all nodes are monitored. The concept was introduced in the context of electrical networks but has been extended and studied for other networks and families of graphs. It has been shown that this problem is NP-complete and thus, for large networks, optimization methods like simulated annealing, threshold acceptance or genetic algorithms could be useful to find near-optimal solutions. In this TFG we introduce a new threshold acceptance algorithm to find power domination sets in graphs and we apply it to analyze these sets in relation to airport centralities and cascade failures in the European airport network. To start with, the cited network is analyzed using a few distinct centrality definitions, including a classical degree centrality, betweenness centrality PageRank, etc. to find the most connected nodes and have an overview of the whole network. An alternative outlook of the local connectivity between nodes is given by finding communities. These groups of nodes are identified according to their strong local associations, in opposition to weaker associations with the rest of the nodes. Having characterised the network from different perspectives, cascade failures are modelled to detect vulnerabilities on the network by comparing the effects of different airport closures. A comparison is assessed based on the effect of the failure of airports depending on their classification. Failing nodes could belong to power dominations sets or be nodes selected from high, medium or low connectivity levels. The main result is a complete insight on how the system is affected from the failure of nodes according to their properties and how the parameters used to tune the model affect this analysis.
Un conjunt dominador en potència (power dominating set) en una xarxa és un
subconjunt de nodes que poden monitoritzar la totalitat de la xarxa a partir d’un
conjunt de regles senzilles. El concepte s’introduí en el context de les xarxes
elèctriques, però s’ha estès i estudiat per a altres xarxes i famílies de grafs.
S’ha demostrat que aquest problema és NP-complet pel que, per xarxes grans,
mètodes d’optimització com la recuita simulada (simulated annealing),
threshold accepting o algorismes genètics constitueixen eines útils per poder
trobar solucions òptimes o quasi-òptimes
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