Related papers: Tree Projections and Structural Decomposition Meth…

Treewidth is a parameter that emerged from the study of minor closed classes of graphs (i.e. classes closed under vertex and edge deletion, and edge contraction). It in some sense describes the global structure of a graph. Roughly, a graph…

This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…

The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted…

Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…

Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with $\omega$-regular winning conditions, specified as parity objectives, which can express properties…

Decomposition methods have been proposed to approximate solutions to large sequential decision making problems. In contexts where an agent interacts with multiple entities, utility decomposition can be used to separate the global objective…

This paper deals with the construction of a correlation decay tree (hypertree) for interacting systems modeled using graphs (hypergraphs) that can be used to compute the marginal probability of any vertex of interest. Local message passing…

This paper offers a new authentication algorithm based on image matching of nano-resolution visual identifiers with tree-shaped patterns. The algorithm includes image-to-tree conversion by greedy extraction of the fractal pattern skeleton…

We prove that every graph which admits a tree-decomposition into finite parts has a rooted tree-decomposition into finite parts that is linked, tight and componental. As an application, we obtain that every graph without half-grid minor has…

This paper explores the structure of graphs defined by an excluded minor or an excluded odd minor through the lens of graph products and tree-decompositions. We prove that every graph excluding a fixed odd minor is contained in the strong…

In the classical (min-cost) Steiner tree problem, we are given an edge-weighted undirected graph and a set of terminal nodes. The goal is to compute a min-cost tree S which spans all terminals. In this paper we consider the min-power…

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…

The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an…

We present an easy structure theorem for graphs which do not admit an immersion of the complete graph. The theorem motivates the definition of a variation of tree decompositions based on edge cuts instead of vertex cuts which we call…

An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…

Decomposition methods are often used for producing counterfactual predictions in non-strategic settings. When the outcome of interest arises from a game-theoretic setting where agents are better off by deviating from their strategies after…

Several algorithms build on the perfect phylogeny model to infer evolutionary trees. This problem is particularly hard when evolutionary trees are inferred from the fraction of genomes that have mutations in different positions, across…

There are many results asserting the existence of tree-decompositions of minimal width which still represent local connectivity properties of the underlying graph, perhaps the best-known being Thomas' theorem that proves for every graph $G$…

In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…