Related papers: Tree Projections and Structural Decomposition Meth…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
When does a graph admit a tree-decomposition in which every bag has small diameter? For finite graphs, this is a property of interest in algorithmic graph theory, where it is called having bounded ``tree-length''. We will show that this is…
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
Structural subtyping and parametric polymorphism provide similar flexibility and reusability to programmers. For example, both features enable the programmer to provide a wider record as an argument to a function that expects a narrower…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, $\mu\text{-}tw$, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…
Tree-decompositions and treewidth are of fundamental importance in structural and algorithmic graph theory. The "spread" of a tree-decomposition is the minimum integer $s$ such that every vertex lies in at most $s$ bags. A…
Cops and Robbers is a pursuit evasion game played on a graph, first introduced independently by Quilliot \cite{quilliot1978jeux} and Nowakowski and Winkler \cite{NOWAKOWSKI1983235} over four decades ago. A main interest in recent the…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry,…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed…
We propose a Reinforcement Learning based approach to approximately solve the Tree Decomposition (TD) problem. TD is a combinatorial problem, which is central to the analysis of graph minor structure and computational complexity, as well as…
We introduce and study the problem of planning a trajectory for an agent to carry out a scouting mission while avoiding being detected by an adversarial guard. This introduces an adversarial version of classical visibility-based planning…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
We present the notion of separable game with respect to a forward directed hypergraph (FDH-graph), which refines and generalizes that of graphical game. First, we show that there exists a minimal FDH-graph with respect to which a game is…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…