Related papers: Graph-Theoretic Solutions to Computational Geometr…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…