Data-Structure Rewriting

We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a pattern, as well as adding new information to an existing data ; and (ii) Global Redirection steps which are aimed to redirect all pointers targeting a node towards another one. We define these two rewriting steps following the double pushout approach. We define first the category of graphs we consider and then define rewrite rules as pairs of graph homomorphisms of the form "L R". Unfortunately, inverse pushouts (complement pushouts) are not unique in our setting and pushouts do not always exist. Therefore, we define rewriting steps so that a rewrite rule can always be performed once a matching is found

On Low Treewidth Approximations of Conjunctive Queries

We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed to exist. However, while for acyclic and bounded hypertreewidth queries we have shown a number of examples of interesting approximations, for queries of bounded treewidth the study had been restricted to queries over graphs, where such approximations usually trivialize. In this note we show that for relations of arity greater than two, the notion of low treewidth approximations is a rich one, as many queries possess them. In fact we look at approximations of queries of maximum possible treewidth by queries of minimum possible treewidth (i.e., one), and show that even in this case the structure of approximations remain rather rich as long as input relations are not binary

Disproof of the List Hadwiger Conjecture

The List Hadwiger Conjecture asserts that every $K_t$-minor-free graph is $t$-choosable. We disprove this conjecture by constructing a $K_{3t+2}$-minor-free graph that is not $4t$-choosable for every integer $t\geq 1$