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Inapproximability of Shortest Paths on Perfect Matching Polytopes
We consider the computational problem of finding short paths in the skeleton of the perfect matching polytope of a bipartite graph. We prove that...
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On Permuting Some Coordinates of Polytopes
Let \(P\subseteq \mathbb {R}^{d}\) be a...
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Toric Fiber Products in Geometric Modeling
An important challenge in Geometric Modeling is to classify polytopes with rational linear precision. Equivalently, in Algebraic Statistics one is...
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Morphogenetic computing: computability and complexity results
A morphogenetic (M) system is an abstract computational model combining properties of membrane (P) systems, such as computing via abstract particles...
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Algebraic Polytopes in Normaliz
We describe the implementation of algebraic polyhedra in Normaliz. In addition to convex hull computation/vertex enumeration, Normaliz computes...
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Provable Preimage Under-Approximation for Neural Networks
Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given...
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Constrained polynomial zonotopes
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian...
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An Algorithm for Polytope Overlap** Detection
The intersection of polytopes is a basic problem of computational geometry with many engineering applications. Intersections of simplices or...
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Theoretical Bounds on Data Requirements for the Ray-Based Classification
The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of...
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Prologue
This is the prelude to a new beginning in approaching a difficult combinatorial optimisation problem (COP), like the symmetric travelling salesman...
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Backtracking Algorithms for Constructing the Hamiltonian Decomposition of a 4-Regular Multigraph
AbstractWe consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that...
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Trainability and real-world knowledge
Until this point, we concentrated on the lexicon, conceived of as the repository of shared linguistic information. In 8.1 we take on the problem of...
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The Octatope Abstract Domain for Verification of Neural Networks
Efficient verification algorithms for neural networks often depend on various abstract domains such as intervals, zonotopes, and linear star sets....
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Properties of Multipyramidal Elements
The finite element method is based on the division of the physical domains into a large number of small polytopes with simple geometry. Basically,...
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K-polytopes: a superproblem of k-means
It has already been proven that under certain circumstances dictionary learning for sparse representations is equivalent to conventional k -means...
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Model Checking HPnGs in Multiple Dimensions: Representing State Sets as Convex Polytopes
Hybrid Petri Nets with general transitions (HPnG) include general transitions that fire after a randomly distributed amount of time. Stochastic Time...
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Extended Formulations for Stable Set Polytopes of Graphs Without Two Disjoint Odd Cycles
Let G be an n-node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC’17) for bimodular integer programs...
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Shape modeling with spline partitions
Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus...
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SyReNN: A tool for analyzing deep neural networks
Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Unfortunately, modern DNNs have been shown to be...
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Formal Methods for Robot Motion Planning with Time and Space Constraints (Extended Abstract)
Motion planning is one of the core problems in a wide range of robotic applications. We discuss the use of temporal logics to include complex...