More algorithmic results for problems of spread of influence in edge-weighted graphs with and without incentives

Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and edges represent social ties between elements. A main problem is to study important subsets of elements (target sets or dynamic monopolies) such that their activation spreads to the entire network. In edge-weighted networks the influence between two adjacent vertices depends on the weight of their edge. In models with incentives, the main problem is to minimize total amount of incentives (called optimal target vectors) which can be offered to vertices such that some vertices are activated and their activation spreads to the whole network. Algorithmic study of target sets and vectors is a hot research field. We prove an inapproximability result for optimal target sets in edge weighted networks even for complete graphs. Some other hardness and polynomial time results are presented for optimal target vectors and degenerate threshold assignments in edge-weighted networks.