Related papers: Removing Local Extrema from Imprecise Terrains
We consider several problems related to packing forests in graphs. The first one is to find $k$ edge-disjoint forests in a directed graph $G$ of maximal size such that the indegree of each vertex in these forests is at most $k$. We describe…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…
(I) We revisit the algorithmic problem of finding all triangles in a graph $G=(V,E)$ with $n$ vertices and $m$ edges. According to a result of Chiba and Nishizeki (1985), this task can be achieved by a combinatorial algorithm running in…
We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by…
Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate: (i) how global minima with zero generalization error…
We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $\tau_\rho$, are there $k$ edges…
Given $n$ points in a circular region $C$ in the plane, we study the problems of moving the $n$ points to its boundary to form a regular $n$-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the…
Understanding the loss surface of neural networks is essential for the design of models with predictable performance and their success in applications. Experimental results suggest that sufficiently deep and wide neural networks are not…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted…
Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…
Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…
Since 1997 there has been a steady stream of advances for the maximum disjoint paths problem. Achieving tractable results has usually required focusing on relaxations such as: (i) to allow some bounded edge congestion in solutions, (ii) to…
A mobile robot represented by a point moving in the plane has to explore an unknown terrain with obstacles. Both the terrain and the obstacles are modeled as arbitrary polygons. We consider two scenarios: the unlimited vision, when the…
In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…