Related papers: A Search Algorithm for Simplicial Complexes
A simplicial vertex of a graph is a vertex whose neighborhood is a clique. It is known that listing all simplicial vertices can be done in $O(nm)$ time or $O(n^{\omega})$ time, where $O(n^{\omega})$ is the time needed to perform a fast…
this paper presents an enhancement of the medial axis algorithm to be used for finding the optimal shortest path for developed cognitive map. The cognitive map has been developed, based on the architectural blueprint maps. The idea for…
We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P. Path P…
In the decremental single-source shortest paths (SSSP) problem, the input is an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges undergoing edge deletions, together with a fixed source vertex $s\in V$. The goal is to maintain a…
In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…
We present a new approach called GR (Graph Reduction) algorithm for searching loop-less k-shortest paths (1st to k-th shortest paths) in a graph based on graph reduction. Let a source vertex and a target vertex of k-shortest paths be v_s…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set $S$ of point sites in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
The neighbourhood matrix, $\mathcal{NM}(G)$, a novel representation of graphs proposed in \cite {ALPaper} is defined using the neighbourhood sets of the vertices. The matrix also exhibits a bijection between the product of two well-known…
GPS receivers embedded in cell phones and connected vehicles generate a series of location measurements that can be used for various analytical purposes. A common pre-processing step of this data is the so-called map matching. The goal of…
Autonomous vehicle navigation in structured environments requires planners capable of generating time-optimal, collision-free trajectories that satisfy dynamic and kinematic constraints. We introduce V*, a graph-based motion planner that…
For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection…
Graphs of Convex Sets (GCS) is a recent method for synthesizing smooth trajectories by decomposing the planning space into convex sets, forming a graph to encode the adjacency relationships within the decomposition, and then simultaneously…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Motion planning is the core problem to solve for developing any application involving an autonomous mobile robot. The fundamental motion planning problem involves generating a trajectory for a robot for point-to-point navigation while…
Finding the shortest path between two points in a graph is a fundamental problem that has been well-studied over the past several decades. Shortest path algorithms are commonly applied to modern navigation systems, so our study aims to…
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…
Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…
We give the first parallel algorithm with optimal $\tilde{O}(m)$ work for the classical problem of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In graphs without negative edges, Dijkstra's algorithm…