Related papers: An Experimental Study of the Treewidth of Real-Wor…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite different. The theorem asserts a duality…
For any small positive real $\varepsilon$ and integer $t > \frac{1}{\varepsilon}$, we build a graph with a vertex deletion set of size $t$ to a tree, and twin-width greater than $2^{(1-\varepsilon) t}$. In particular, this shows that the…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We introduce 'project-connex' tree-width as a measure of tractability for counting and aggregate conjunctive queries over semirings with 'group-by' projection (also known as 'AJAR' or 'FAQ' queries). This elementary measure allows to obtain…
It is known for many algorithmic problems that if a tree decomposition of width $t$ is given in the input, then the problem can be solved with exponential dependence on $t$. A line of research by Lokshtanov, Marx, and Saurabh [SODA 2011]…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
We study two graph parameters defined via tree decompositions: tree-independence number and induced matching treewidth. Both parameters are defined similarly as treewidth, but with respect to different measures of a tree decomposition…
We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We…
Many data sets, crucial for today's applications, consist essentially of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…
Tree-width and path-width are widely successful concepts. Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width. Many efficient algorithms are based on a tree decomposition. Sometimes the more…
Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \emph{algorithmically useful} i.e. admitting polynomial-time algorithms for…
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and…
The gradual patterns that model the complex co-variations of attributes of the form "The more/less X, The more/less Y" play a crucial role in many real world applications where the amount of numerical data to manage is important, this is…
We prove that the (divisorial) gonality of a finite connected graph is lower bounded by its treewidth. We show that equality holds for grid graphs and complete multipartite graphs. We prove that the treewidth lower bound also holds for…
This work proposes \textsc{H-Td}, a practical linear-time algorithm for computing an optimal-width tree decomposition of Halin graphs. Unlike state-of-the-art methods based on reduction rules or separators, \textsc{H-Td} exploits the…
We obtain structure theorems for graphs excluding a fan (a path with a universal vertex) or a dipole ($K_{2,k}$) as a topological minor. The corresponding decompositions can be computed in FPT linear time. This is motivated by the study of…