Related papers: Inverting the Sweep Map on (2n,n)-Dyck Paths: A Si…

This paper gives an introduction to the problem of mapping simple polygons with autonomous agents. We focus on minimalistic agents that move from vertex to vertex along straight lines inside a polygon, using their sensors to gather local…

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…

It is known that both the number of Dyck paths with $2n$ steps and $k$ peaks, and the number of Dyck paths with $2n$ steps and $k$ steps at odd height follow the Narayana distribution. In this paper we present a bijection which explicitly…

Let $S$ be a planar point set in general position, and let $\mathcal{P}(S)$ be the set of all plane straight-line paths with vertex set $S$. A flip on a path $P \in \mathcal{P}(S)$ is the operation of replacing an edge $e$ of $P$ with…

Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of…

A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D…

Essential tasks in autonomous driving includes environment perception, detection and tracking, path planning and action control. This paper focus on path planning, which is one of the challenging task as it needs to find optimal path in…

Finding k disjoint paths (kDP) is a fundamental problem in graph analysis. For vertices s and t, paths from s to t are said to be disjoint if any two of them share no common vertex except s and t. In practice, disjoint paths are widely…

In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…

The aim of this research is to reconstruct the 3D X-ray refractive index gradient maps by the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses show that the…

This paper proposes a novel inverse kinematics (IK) solver of articulated robotic systems for path planning. IK is a traditional but essential problem for robot manipulation. Recently, data-driven methods have been proposed to quickly solve…

Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation properties of INNs have also been established recently.…

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…

Given a simple graph $G = (V, E)$ and a constant integer $k \ge 2$, the $k$-path vertex cover problem ({\sc P$k$VC}) asks for a minimum subset $F \subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path…

We propose Ky Fan 2-k-norm-based models for the nonconvex low-rank matrix recovery problem. A general difference of convex algorithm (DCA) is developed to solve these models. Numerical results show that the proposed models achieve high…

We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…

A version of Dehn's algorithm for simple diagrams on a once punctured surface representing simple diagrams on a closed surface is presented

In the $k$-Disjoint Shortest Paths ($k$-DSP) problem, we are given a weighted graph $G$ on $n$ nodes and $m$ edges with specified source vertices $s_1, \dots, s_k$, and target vertices $t_1, \dots, t_k$, and are tasked with determining if…

The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…