Final Activity Report Summary - GAMA (Graph algorithms and massive data sets) A graph is a basic combinatorial structure consisting of a set of so-called vertices and a set of links between some pairs of the vertices. A typical example of graph is: each person in the world is a vertex, and each pair of persons is linked if they know each other (or if they are relatives or any other property one may choose). In particular, graphs are a generalisation of networks. The distance between two vertices of a graph is defined as the minimum number of links you have to follow to go from one vertex to the other one.A drawing (in the plane) of a graph is a representation where each vertex is assigned a point and each link is a path joining its vertices. Planar graphs, that is, graphs that can be drawn without two links crossing, are an important class of graphs that has been extensively studied before. They enjoy a rich amount of properties and structure, but, more importantly, they arise in many applications. An extension of planar graphs is graphs on surfaces, that is, graphs that can be drawn in a fixed surface without two links crossing each other.The objective of this project was to obtain new, efficient algorithms for solving problems whose input is a graph. Large part of the project has been devoted to algorithms for planar graphs and graphs on surfaces, and, more precisely, problems concerning distances. Several new results and techniques devoted to this area have been obtained. As a major achievement, we have shown how to improve the trade-off between the time needed to preprocess a planar graph and the time needed to report distances between its vertices.
