Related papers: Tree Projections and Structural Decomposition Meth…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of…
The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the…
Human behavior emerges from planning over elaborate decompositions of tasks into goals, subgoals, and low-level actions. How are these decompositions created and used? Here, we propose and evaluate a normative framework for task…
Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
At the core of the Robertson-Seymour theory of graph minors lies a powerful structure theorem which captures, for any fixed graph H, the common structural features of all the graphs not containing H as a minor. Robertson and Seymour prove…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\v{s}ov\'{a}…
Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems…
\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory.…
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…
Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
We here investigate on the complexity of computing the \emph{tree-length} and the \emph{tree-breadth} of any graph $G$, that are respectively the best possible upper-bounds on the diameter and the radius of the bags in a tree decomposition…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…