Download or read book Query Enumeration and Nowhere Dense Graphs written by Alexandre Vigny and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of my thesis lies between complexity, algorithmic and logic. In particular, we are interested in the complexity of evaluating query.More precisely, given G a finite graph. A query q defines a subset of k-tuples of vertices of G that we note q(G). We call k the arity of q and we then try to efficiently perform the following tasks:1) decide whether the set q G) is empty.2) decide whether a given k-tuplet belongs to the set of solutions q(G).3) calculate the number of solutions.4) enumerate the elements of q(G).Regarding the 4th task, an algorithm that will enumerate the solutions can be decomposed into two steps. The first is called preprocessing and is used to prepare the enumeration. Ideally this step only requires a time linear in the size of the graph. The second step is the enumeration properly speaking. The time needed to get a new solution is called the delay. Ideally we want the delay to not depend on the size of the graph but only on the size of the query. We then talk about constant delay enumeration after linear preprocessing.At the beginning of this thesis, a large part of the interrogations about classes of graphs for which a constant delay enumeration is possible seemed to be located around the classes of nowhere dense graphs.