Related papers: Efficient Fastest-Path Computations in Road Maps
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
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…
Robot path planning plays a pivotal role in enabling autonomous systems to navigate safely and efficiently in complex and uncertain environments. Despite extensive research on classical graph-based methods and sampling-based planners,…
Although Dijkstra's algorithm has near-optimal time complexity for the problem of finding a shortest path from a given vertex $s$ to a given vertex $t$, in practice other algorithms are often superior on huge graphs. A prominent example is…
Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…
Exact computation of shortest paths in weighted graphs has been traditionally studied in one of two settings. First, one can assume that the edge weights are real numbers and all the performed operations on reals (typically comparisons and…
In this paper, we tackle the problem of risk-averse route planning in a transportation network with time-dependent and stochastic costs. To solve this problem, we propose an adaptation of the A* algorithm that accommodates any risk measure…
In imitation learning for planning, parameters of heuristic functions are optimized against a set of solved problem instances. This work revisits the necessary and sufficient conditions of strictly optimally efficient heuristics for forward…
We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph $G=(V,E)$ with a positive real weight on each edge. We present two fully dynamic…
Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow,…
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…
We present two methods to compress the description of a route in a road network, i.e., of a path in a directed graph. The first method represents a path by a sequence of via edges. The subpaths between the via edges have to be unique…
We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…
We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…
The widespread use of graph data in various applications and the highly dynamic nature of today's networks have made it imperative to analyze structural trends in dynamic graphs on a continual basis. The shortest path is a fundamental…
This paper presents a pipeline that combines high-resolution orthomosaic maps generated from UAS imagery with GPS-based global navigation to guide a skid-steered ground robot. We evaluated three path planning strategies: A* Graph search,…
We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to…
In a directed graph $G=(V,E)$ with a capacity on every edge, a \emph{bottleneck path} (or \emph{widest path}) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
In this paper we show a deterministic parallel all-pairs shortest paths algorithm for real-weighted directed graphs. The algorithm has $\tilde{O}(nm+(n/d)^3)$ work and $\tilde{O}(d)$ depth for any depth parameter $d\in [1,n]$. To the best…