Related papers: An Experimental Study of Algorithms for Geodesic S…
We study the generalized minimum Manhattan network (GMMN) problem: given a set $P$ of pairs of two points in the Euclidean plane $\mathbb{R}^2$, we are required to find a minimum-length geometric network which consists of axis-aligned…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
We present an algorithm to explore an orthogonal polygon using a team of $p$ robots. This algorithm combines ideas from information-theoretic exploration algorithms and computational geometry based exploration algorithms. We show that the…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
We study the problem of learning a binary classifier on the vertices of a graph. In particular, we consider classifiers given by monophonic halfspaces, partitions of the vertices that are convex in a certain abstract sense. Monophonic…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
Python implementation of selected weighted graph algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are…
We study the Shortest-Walk Problem (SWP) in a Graph of Convex Sets (GCS). A GCS is a graph where each vertex is paired with a convex program, and each edge couples adjacent programs via additional costs and constraints. A walk in a GCS is a…
We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms…
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…
We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We consider single-source shortest path algorithms that perform a sequence of relaxation steps whose ordering depends only on the input graph structure and not on its weights or the results of prior steps. Each step examines one edge of the…
We analyze the popular ``state-space'' class of algorithms for detecting casual interaction in coupled dynamical systems. These algorithms are often justified by Takens' embedding theorem, which provides conditions under which relationships…