An extension of labeling techniques for finding shortest path trees (original) (raw)
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A minimum weight labelling method for determination of a shortest route in a non-directed network
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The Shortest-Path Problem: Analysis and Comparison of Methods
Synthesis Lectures on Theoretical Computer Science, 2014
Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology.
Journal of Mathematics Research
In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10 and 1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.
Review and Performance Analysis of Shortest Path Problem Solving Algorithms
The International Journal on Advances in Software, ISSN: 1942-2628, vol. 7, no. 1& 2,year 2014,, 2014
The development of concepts derived from the generic approach to solving the problem of the shortest path resulted in numerous and various algorithms that appeared over the past decades. The studies on the most basic operation aimed at the determination of the shortest path between two given points in a graph (in other words, often a network) have resulted in sophisticated solutions designed for more and more demanding applications. Those include finding the sets of paths with the shortest distance between all pairs of nodes or searching for a shortest path tree. The aim of the present article is to give the reader an introduction to the problem of the shortest path and a detailed review of two groups of selected algorithms designed to solve particular problems. In the study described herein, different algorithms have been examined for their efficacy in their operation in directed graphs of different type represented in a well-defined data structure. The empirical simulation-based analysis proves that the performance varies among algorithms under investigation and allows to suggest, which methods ought to be used to solve specific variants of the shortest path problem and which algorithms should be avoided or used with caution.
Shortest Path Algorithms: Comparative Study and Analysis
shortest path problem is a fundamental technique in computer networking for route discovery. Utilizing the shortest path algorithms overall costs of setting the network is reduced. Many new technologies are implemented using the shortest path problem e.g. the road map system. Shortest path problem is an optimization technique [1] used in many applications. In this paper's different shortest path algorithms are studied i.e. Dijkstra's Algorithm, A* Search, FloydWarshall Algorithm, Johnson's Algorithm and Bellman-Ford Algorithm. We will study or analyze the behavior of different algorithms of shortest path in this paper. First we will study each algorithm to analyze its performance and then we will compare algorithms on the basis of their time complexity.
A Heuristic Graph-Based Shortest Path Algorithm for Optimizing Routing Problems
Route optimization is a process of considering all possible routes connecting the source and the destination and looks at the heuristic cost of each route and selecting the least cost route. Route planners depend principally on past occurrence of events associated with route optimization; hence they often use local knowledge, simple procedures, and ad hoc procedures to optimize the routes. In this paper, we proposed a graph-based shortest path algorithm for optimizing route directory. The algorithm is based on the Dijkstra algorithm. It is an improved shortest-path algorithm proposed as initially proposed by Dijkstra. In order to determine the shortest route and the most cost effective route, the algorithm is used to determine the shortest path that a traveler or someone going to a particular destination for the first time. The algorithm is tested by comparing its results with existing route algorithms and the results are presented and discussed.
A Survey of Shortest-Path Algorithms
ArXiv, 2017
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path problem. There is no one general algorithm that is capable of solving all variants of the shortest-path problem due to the space and time complexities associated with each algorithm. Other important dimensions of the taxonomy include whether the shortest-path algorithm operates over a static or a dynamic graph, whether the shortest-path algorithm produces exact or approximate answers, and whether the objective of the shortest-path algorithm is to achieve time-dependence or is to only be goal directed. This survey studies and classifies shortest-path algorithms according to the proposed taxonomy. Th...
Comparison Studies for Different Shortest path Algorithms
International Journal of Computers Technology, 2015
While technological revolution has active role to the increase of computer information, growing computational capabilities of devices, and raise the level of knowledge abilities, and skills. Increase developments in science and technology. In graph used the shortest path algorithms for solving the shortest path problem. The shortest path can be single pair shortest path problem or all pairs shortest path problem. This paper discuss briefly the shortest path algorithms such as Dijkstra's algorithm, Bellman-Ford algorithm,Floyd-Warshall algorithm, and johnson's algorithm. It describes the previous algorithms for solving the shortest path problem. The goal of this paper is to investigate and comparison the impacts of different shortest path algorithms. The study shows that the efficiency varies among algorithms, helps to suggest which one of them ought to be used to solve a specific variant of the shortest path problem.
Shortest Path Algorithms between Theory and Practice
MSc Thesis, 2019
Utilizing graph algorithms is a common activity in computer science. Algorithms that perform computations on large graphs are not always efficient. This work investigates the Single-Source Shortest Path (SSSP) problem, which is considered to be one of the most important and most studied graph problems. This thesis contains a review of the SSSP problem in both theory and practice. In addition, it discusses a new single-source shortest-path algorithm that achieves the same O(ncdotm)O(n \cdot m)O(ncdotm) time bound as the traditional Bellman-Ford-Moore algorithm but outperforms it and other state-of-the-art algorithms in practice. The work is comprised of three parts. The first discusses some basic shortest-path and negative-cycle-detection algorithms in literature from the theoretical and practical point of view. The second contains a discussion of a new algorithm for the single-source shortest-path problem that outperforms most state-of-the-art algorithms for several well-known families of graphs. The main idea behind the proposed algorithm is to select the fewest most-effective vertices to scan. We also propose a discussion of correctness, termination, and the proof of the worst-case time bound of the proposed algorithm. This section also suggests two different implementations for the proposed algorithm, the first runs faster while the second performs a fewer number of operations. Finally, an extensive computational study of the different shortest paths algorithms is conducted. The results are proposed using a new evaluation metric for shortest-path algorithms. A discussion of outcomes, strengths, and weaknesses of the various shortest path algorithms are also included in this work.