Related papers: An impossible utopia in distance geometry
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
Distance geometry explores the properties of distance spaces that can be exactly represented as the pairwise Euclidean distances between points in $\mathbb{R}^d$ ($d \geq 1$), or equivalently, distance spaces that can be isometrically…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
The \emph{$r$-neighbourhood complexity} of a graph $G$ is the function counting, for a given integer $k$, the largest possible number, over all vertex-subsets $A$ of size $k$, of subsets of $A$ realized as the intersection between the…
In the $k$-Center problem, we are given a graph $G=(V,E)$ with positive edge weights and an integer $k$ and the goal is to select $k$ center vertices $C \subseteq V$ such that the maximum distance from any vertex to the closest center…
In this work, we explore heuristics for the Adjacency Graph Packing problem, which can be applied to the Double Cut and Join (DCJ) Distance Problem. The DCJ is a rearrangement operation and the distance problem considering it is a well…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
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…
Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich…
Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph…
We address discrete-time consensus on the Euclidean unit sphere. For this purpose we consider a distributed algorithm comprising the iterative projection of a conical combination of neighboring states. Neighborhoods are represented by a…
We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex $u$, a target vertex $v$ and a set $X$ of $k$ failed vertices, such an oracle returns the length of a shortest…
We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define…
Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parametrized by joint angles, generating a complicated…
We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O(n)$ distances to output a constant factor approximation to the average distance among those points, thus answering a…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is…