Related papers: Computing Hive Plots: A Combinatorial Framework
Heffter arrays were introduced by Archdeacon in 2015 as an interesting link between combinatorial designs and topological graph theory. Since the initial paper on this topic, there has been a good deal of interest in Heffter arrays as well…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a…
Rapid development of evolutionary algorithms in handling many-objective optimization problems requires viable methods of visualizing a high-dimensional solution set. Parallel coordinates which scale well to high-dimensional data are such a…
In ensemble methods, the outputs of a collection of diverse classifiers are combined in the expectation that the global prediction be more accurate than the individual ones. Heterogeneous ensembles consist of predictors of different types,…
Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…
Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical…
This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular…
We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…
High-dimensional motion planning problems can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles.…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past…
We introduce and systematically study \emph{hierarchical filtrations} of vector bundles on smooth projective varieties. These are filtrations by saturated subsheaves of equal rank whose successive quotients are torsion sheaves supported in…
The paper describes combinatorial framework for planning of geological exploration for oil-gas fields. The suggested scheme of the geological exploration involves the following stages: (1) building of special 4-layer tree-like model (layer…