The Shortest-Path Problem: Analysis and Comparison of Methods (original) (raw)

Shortest Path Algorithms: An Evaluation Using Real Road Networks

Transportation Science, 1998

The classic problem of finding the shortest path over a network has been the target of many research efforts over the years. These research efforts have resulted in a number of different algorithms and a considerable amount of empirical findings with respect to performance. Unfortunately, prior research does not provide a clear direction for choosing an algorithm when one faces the problem of computing shortest paths on real road networks. Most of the computational testing on shortest path algorithms has been based on randomly generated networks, which may not have the characteristics of real road networks. In this paper, we provide an objective evaluation of 15 shortest path algorithms using a variety of real road networks. Based on the evaluation, a set of recommended algorithms for computing shortest paths on real road networks is identified. This evaluation should be particularly useful to researchers and practitioners in operations research, management science, transportation, ...

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.

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.

A Novel Solution for Simultaneously Finding the Shortest and Possible Paths in Complex Networks

2019

A Novel graph approach named Combined Forward and Backward Heuristic Search (CFBHS) is proposed in this paper, which can be used to solve optimization problems in areas such as transportation and network routing. There are two major aspects distinct our method from the most cited ones. Firstly, though focuses on getting the shortest path in a graph when both source and destination are given, this work can also find other possible paths as outputs. Secondly, the proposed algorithm is a high-performance one, which is achieved by (1) reducing unnecessary nodes and edges to reach a target optimum based on dynamically calculated heuristic values and (2) finding the results by using the sub-division scheme instead of computing over the whole graph. Experiments are carried out for the complex road network of Yangon Region. The comparisons show that our algorithm is about 100 times faster than the bi-directional Dijkstra’s algorithm. Besides, benefit from the heuristic forward and backward ...

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.

Finding shortest paths on real road networks: the case for A*

International Journal of Geographical Information Science, 2009

The problem of identifying the shortest path along a road network is a fundamental problem in network analysis, ranging from route guidance in a navigation system to solving spatial allocation problems. Since this type of problem is solved so frequently, it is important to craft an approach that is as efficient as possible. Based upon past research it is generally accepted that several efficient implementations of the Dijkstra algorithm are the fastest at optimally solving the 'one-to-one' shortest path problem (Cherkassky, et al. 1996). We show that the most efficient, state-of-the-art implementations of Dijkstra can be improved by taking advantage of network properties associated with GIS-sourced data. The results of this paper, derived from tests of different algorithmic approaches on real road networks, will be extremely valuable for application developers and researchers in the GIS community.

Heuristic shortest path algorithms for transportation applications- State of the art

There are a number of transportation applications that require the use of a heuristic shortest path algorithm rather than one of the standard, optimal algorithms. This is primarily due to the requirements of some transportation applications where shortest paths need to be quickly identified either because an immediate response is required (e.g., in-vehicle route guidance systems) or because the shortest paths need to be recalculated repeatedly (e.g., vehicle routing and scheduling). For this reason a number of heuristic approaches have been advocated for decreasing the computation time of the shortest path algorithm. This paper presents a survey review of various heuristic shortest path algorithms that have been developed in the past. The goal is to identify the main features of different heuristic strategies, develop a unifying classification framework, and summarize relevant computational experience.

IJERT-A Study on Different Algorithms for Shortest Route Problem

International Journal of Engineering Research and Technology (IJERT), 2013

https://www.ijert.org/a-study-on-different-algorithms-for-shortest-route-problem https://www.ijert.org/research/a-study-on-different-algorithms-for-shortest-route-problem-IJERTV2IS90327.pdf Shortest path problems are among the most studied network flow optimization problems with interesting application across a range of fields. In this paper, three shortest path algorithms are discussed viz. Dijkstra's Algorithm (one to all pairs of nodes), Floyd Warshall's Algorithm (all to all pairs of nodes) and Linear Programming Problems (LPP). These algorithms are also solved using Matlab software, which gives quick results for larger nodes. This paper also deals with the methodology to find shortest distance using the dual of Linear Programming Problems. In addition, Complementary Slackness Theorem is discussed to solve the primal problem from the solution of dual problem and determine the shortest distance as well as shortest routes.

Computing the shortest path: A search meets graph theory

… of the sixteenth annual ACM-SIAM …, 2005

We study the problem of finding a shortest path between two vertices in a directed graph. This is an important problem with many applications, including that of computing driving directions. We allow preprocessing the graph using a linear amount of extra space to store auxiliary information, and using this information to answer shortest path queries quickly. Our approach uses A * search in combination with a new graph-theoretic lower-bounding technique based on landmarks and the triangle inequality. We also develop new bidirectional variants of A * search and investigate several variants of the new algorithms to find those that are most efficient in practice. Our algorithms compute optimal shortest paths and work on any directed graph. We give experimental results showing that the most efficient of our new algorithms outperforms previous algorithms, in particular A * search with Euclidean bounds, by a wide margin on road networks. We also experiment with several synthetic graph families.