Related papers: Topology and Routing Problems: The Circular Frame
This paper addresses the problem of a boundary control design for traffic evolving in a large-scale urban network. The traffic state is described on a macroscopic scale and corresponds to the vehicle density, whose dynamics are governed by…
We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity…
Let $P$ be an $x$-monotone orthogonal polygon with $n$ vertices. We call $P$ a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Path Planning and target searching in a three-dimensional environment is a challenging task in the field of robotics. It is an optimization problem as the path from source to destination has to be optimal. This paper aims to generate a…
In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic ``no-slip'' conditions. Using constructs from sub-Riemannian geometry, we look for geodesics corresponding…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
This paper considers the problem of finding a quickest path between two points in the Euclidean plane in the presence of a transportation network. A transportation network consists of a planar network where each road (edge) has an…
Optimal routing in quantum-repeater networks requires finding the best path that connects a pair of end nodes. Most previous work on routing in quantum networks assumes utility functions that are isotonic, meaning that the ordering of two…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
Modern communication networks are increasingly equipped with in-network computational capabilities and services. Routing in such networks is significantly more complicated than the traditional routing. A legitimate route for a flow not only…
In this paper we consider a set of travelers, starting from likely different locations towards a common destination within a road network, and propose solutions to find the optimal connecting points for them. A connecting point is a vertex…
In this paper, we consider a transformation of $k$ disjoint paths in a graph. For a graph and a pair of $k$ disjoint paths $\mathcal{P}$ and $\mathcal{Q}$ connecting the same set of terminal pairs, we aim to determine whether $\mathcal{P}$…
We present Topology-Guided ORCA as an alternative simulator to replace ORCA for planning smooth multi-agent motions in environments with static obstacles. Despite the impressive performance in simulating multi-agent crowd motion in free…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…
We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after…
This paper attacks the following problem. We are given a large number $N$ of rectangles in the plane, each with horizontal and vertical sides, and also a number $r<N$. The given list of $N$ rectangles may contain duplicates. The problem is…