The Power Of Local Computations In Graphs With Initial Knowledge

This paper deals with the delimitation of the power of local computations on graphs having some initial knowledge, e.g. the size or the topology of the network. We refine a proof technique based on coverings in order to cope with additional knowledge. Applying this method we show that several graph properties (e.g., planarity) are not recognizable even if some simple knowledge about the graph (e.g., the size) is available. Similarly, we show that election in ambiguous graphs is impossible, even if the graph topology is known by every node.