Related papers: In the Search for Good Neck Cuts

We study slopes of finite cyclic covering fibrations of a fibered surface. We give the best possible lower bound of the slope of these fibrations. We also give the slope equality of finite cyclic covering fibrations of a ruled surface and…

This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal…

The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…

When searching for interesting structures in graphs, it is often important to take into account not only the graph connectivity, but also the metadata available, such as node and edge labels, or temporal information. In this paper we are…

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

A bottleneck plane perfect matching of a set of $n$ points in $\mathbb{R}^2$ is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as {\em bottleneck}. The…

Lengthy setup processes that require robotics expertise remain a major barrier to deploying robots for tasks involving high product variability and small batch sizes. As a result, collaborative robots, despite their advanced sensing and…

Edge inference has become more widespread, as its diverse applications range from retail to wearable technology. Clusters of networked resource-constrained edge devices are becoming common, yet no system exists to split a DNN across these…

Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or…

We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and smooth algebraic variety using the variety's defining…

In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…

Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among…

Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain.…

Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…

Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Since edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. The reason for this is that edges form the outline of an object. An edge is the…

Motion segmentation is currently an active area of research in computer Vision. The task of comparing different methods of motion segmentation is complicated by the fact that researchers may use subtly different definitions of the problem.…

Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…