scholarly journals Sublinear search spaces for shortest path planning in grid and road networks

2021 ◽  
Author(s):  
Johannes Blum ◽  
Stefan Funke ◽  
Sabine Storandt
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Shortest Paths ◽  
Road Networks ◽  
Grid Graphs ◽  
Search Spaces ◽  
Grid Networks ◽  
Fundamental Building Block ◽  
Important Challenge ◽  
Practical Performance

AbstractShortest path planning is a fundamental building block in many applications. Hence developing efficient methods for computing shortest paths in, e.g., road or grid networks is an important challenge. The most successful techniques for fast query answering rely on preprocessing. However, for many of these techniques it is not fully understood why they perform so remarkably well, and theoretical justification for the empirical results is missing. An attempt to explain the excellent practical performance of preprocessing based techniques on road networks (as transit nodes, hub labels, or contraction hierarchies) in a sound theoretical way are parametrized analyses, e.g., considering the highway dimension or skeleton dimension of a graph. Still, these parameters may be large in case the network contains grid-like substructures—which inarguably is the case for real-world road networks around the globe. In this paper, we use the very intuitive notion of bounded growth graphs to describe road networks and also grid graphs. We show that this model suffices to prove sublinear search spaces for the three above mentioned state-of-the-art shortest path planning techniques. Furthermore, our preprocessing methods are close to the ones used in practice and only require expected polynomial time.

scholarly journals Path Planning for Mobile Agents Using a Genetic Algorithm with a Direction Guided Factor

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 212 ◽  
Author(s):  
Hyeok-Yeon Lee ◽  
Hyunwoo Shin ◽  
Junjae Chae
Keyword(s):  
Genetic Algorithm ◽  
Path Planning ◽  
Shortest Path ◽  
Free Space ◽  
Mobile Agents ◽  
Dimensional Space ◽  
Target Point ◽  
Complex Environments ◽  
Search Spaces ◽  
Starting Point

This paper suggests a novel methodology in collision-free shortest path planning (CFSPP) problems for mobile agents (MAs) using a method that combines a genetic algorithm (GA) and a direction factor toward a target point. In the CFSPP problem, MAs find the shortest path from the starting point to the target point while avoiding certain obstacles. The paper proposes an obstacle-based search methodology that identifies critical collision-free points adjacent to given obstacles. When critical obstacles are found via CFSPP, this study suggests favorable paths in 2-dimensional space found using the obstacle-based GA (OBGA). The OBGA has four advantages. First, it effectively narrows the search spaces compared to free space-based methodologies. It also determines shorter collision-free paths, and it only requires a short amount of time. Finally, convergence occurs more quickly than in previous studies. The proposed method also works properly in larger and more complex environments, indicating that it can be applied to more practical problems.

scholarly journals Finding Shortest Path for Road Network Using Dijkstra’s Algorithm

2019 ◽  
Vol 1 (2) ◽  
pp. 41-45
Author(s):  
Md. Almash Alam ◽  
Md. Omar Faruq
Keyword(s):  
Shortest Path ◽  
Road Network ◽  
Shortest Paths ◽  
Road Networks ◽  
Transportation Systems ◽  
Shortest Path Problem ◽  
Dijkstra’S Algorithm ◽  
Traffic Condition ◽  
Shortest Path Problems ◽  
Dijkstra's Algorithm

Roads play a Major role to the people live in various states, cities, town and villages, from each and every day they travel to work, to schools, to business meetings, and to transport their goods. Even in this modern era whole world used roads, remain one of the most useful mediums used most frequently for transportation and travel. The manipulation of shortest paths between various locations appears to be a major problem in the road networks. The large range of applications and product was introduced to solve or overcome the difficulties by developing different shortest path algorithms. Even now the problem still exists to find the shortest path for road networks. Shortest Path problems are inevitable in road network applications such as city emergency handling and drive guiding system. Basic concepts of network analysis in connection with traffic issues are explored. The traffic condition among a city changes from time to time and there are usually huge amounts of requests occur, it needs to find the solution quickly. The above problems can be rectified through shortest paths by using the Dijkstra’s Algorithm. The main objective is the low cost of the implementation. The shortest path problem is to find a path between two vertices (nodes) on a given graph, such that the sum of the weights on its constituent edges is minimized. This problem has been intensively investigated over years, due to its extensive applications in graph theory, artificial intelligence, computer network and the design of transportation systems. The classic Dijkstra’s algorithm was designed to solve the single source shortest path problem for a static graph. It works starting from the source node and calculating the shortest path on the whole network. Noting that an upper bound of the distance between two nodes can be evaluated in advance on the given transportation network.

A Practical Algorithm for Shortest Paths on Polyhedral Surfaces

1993 ◽  
Author(s):  
P. Rambeaud ◽  
Saïd Zeghloul
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Shortest Paths ◽  
Experimental Results ◽  
Planning Problem ◽  
Polyhedral Surface ◽  
Planning Systems ◽  
Practical Algorithm ◽  
Path Planning Problem ◽  
3D Problem

Abstract This paper describes a method for treating the shortest path planning problem along a convex polyhedral surface using an unfolding process. Since most planning systems use polyhedral environments, finding the shortest possible path is very useful for some typical robotics applications such as spacecraft or submersible robot motions. The basic idea in our algorithm is to unfold the polyhedral surface into a plane, in order to convert the 3D problem to a 2D one. We provide experimental results on a box and on a sphere to illustrate the unfolding process.

scholarly journals RimJump*: Tangent Based Shortest Path Planning for Cluttered 3D Environment

2021 ◽  
Author(s):  
Zhuo Yao
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Autonomous Vehicles ◽  
Shortest Paths ◽  
Research Area ◽  
Time Cost ◽  
Geometrical Properties ◽  
3D Environment ◽  
Starting Point ◽  
Map Scale

Path planning in 3D environment is a fundamental research area for robots and autonomous vehicles. Based on the principle ``the shortest path consists of tangents'', RimJump* is proposed as a tangent-based path planning method suitable for finding the shortest path (both off-ground and on-ground) in 3D space (e.g., octomap and point cloud) for mobile platform to follow. RimJump* searches the tangent graph in the form of a path tree and considers the geometrical properties of the locally shortest path. Therefore, the method can provide all of the locally shortest paths that connect the starting point and the target, including the globally shortest path. And the time cost of RimJump* is insensitive to map scale increases in comparison to methods that search the whole passable space rather than the surface of the obstacle, e.g., Dijkstra and A*. In the Results, RimJump* is compared with other methods in terms of path length and time cost.

scholarly journals Computing nearest neighbour interchange distances between ranked phylogenetic trees

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Lena Collienne ◽  
Alex Gavryushkin
Keyword(s):  
Cancer Research ◽  
Computational Complexity ◽  
Phylogenetic Tree ◽  
Shortest Path ◽  
Phylogenetic Trees ◽  
Shortest Paths ◽  
Nearest Neighbour ◽  
Tree Inference ◽  
Subtree Prune And Regraft ◽  
Comparison Algorithms

AbstractMany popular algorithms for searching the space of leaf-labelled (phylogenetic) trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is $${\mathbf {N}}{\mathbf {P}}$$ N P -hard in each of these graphs, making tree inference and comparison algorithms challenging to design in practice. Although anked phylogenetic trees are one of the central objects of interest in applications such as cancer research, immunology, and epidemiology, the computational complexity of the shortest path problem for these trees remained unsolved for decades. In this paper, we settle this problem for the ranked nearest neighbour interchange operation by establishing that the complexity depends on the weight difference between the two types of tree rearrangements (rank moves and edge moves), and varies from quadratic, which is the lowest possible complexity for this problem, to $${\mathbf {N}}{\mathbf {P}}$$ N P -hard, which is the highest. In particular, our result provides the first example of a phylogenetic tree rearrangement operation for which shortest paths, and hence the distance, can be computed efficiently. Specifically, our algorithm scales to trees with tens of thousands of leaves (and likely hundreds of thousands if implemented efficiently).

scholarly journals Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Christoph Hansknecht ◽  
Imke Joormann ◽  
Sebastian Stiller
Keyword(s):  
Column Generation ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Valid Inequalities ◽  
Shortest Paths ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Full Generality ◽  
Branching Rule ◽  
The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

scholarly journals Path planning for automatic guided vehicle with multiple target points in dynamic environment

2018 ◽  
Vol 159 ◽  
pp. 02029 ◽  
Author(s):  
Chang Kyu Kim ◽  
Huy Hung Nguyen ◽  
Dae Hwan Kim ◽  
Hak Kyeong Kim ◽  
Sang Bong Kim
Keyword(s):  
Path Planning ◽  
Shortest Paths ◽  
Initial Point ◽  
Target Point ◽  
Laser Sensor ◽  
Multiple Target ◽  
Hamilton Path ◽  
Automatic Guided Vehicle ◽  
Planning Algorithm ◽  
Path Planning Algorithm

In path planning field, Automatic guided vehicle (AGV) has to move from an initial point towards a target point with capability to avoid obstacles. There are A*, D* and D* lite path planning algorithms in the path planning algorithm. This paper proposes a modified D* lite path planning algorithm using the most efficient D* lite among these algorithms. The modified D* lite path planning algorithm is to improve these D* lite path planning algorithm’s weaknesses such as traversing across obstacles sharp corners, or traversing between two obstacles. To do this task, the followings are done. First, a work space is divided into square cells. Second, cost of each edge connecting current node to neighbor nodes is calculated. Third, the shortest paths from the initial point to all multiple target points are computed and the shortest paths from any target point to remaining target points including the goal point are computed by using Hamilton path. Fourth, a cost-minimal path is re-calculated as soon as the laser sensor detects an obstacle and make an updated list of target points. Finally, the validity of the proposed modified D* lite path planning algorithm is verified through simulation and experimental results.

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