Graph Models for Optimization Problems in Road Networks

Here two applications of graph theory are considered. The first is devoted to pedestrian safety, and the focus is on pedestrian safety in urban areas with respect to pedestrian-vehicle crashes. In particular, an algorithm for automated construction of a graph model for pavement networks is discussed. Then, an algorithm for finding a user-optimal path in a given pavement network is presented. This algorithm is based on three criteria: path safety, distance, and path complexity. The second part of this chapter is devoted to optimizing the placement of charging stations for electric vehicles in road networks. The placement of charging stations in road networks is modelled as a multiple domination problem on reachability graphs. This model takes into account a threshold for the remaining battery charge and provides some minimal choice for a travel direction to recharge the battery. Experimental evaluation and simulations for the proposed facility location model are given for real road networks of the cities of Boston and Dublin.