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Towards Online Shortest Path using

Dijkstra Algorithm

                  Neha Makariye                                               Deepa Deshpande

   (Master of Engg)  Dr.B.A.M.University, Aurangabad        Dr.B.A.M.University, Aurangabad

                 [email protected]                                            [email protected]

             

Abstract- 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. Shortest Path problem aims at computing the shortest path based on traf'c circumstances and gives the best path. This is very important in modern navigation systems as it can help to make sensible decisions. This approach has excellent scalability with the number of clients. Thus, it develops a new framework called towards online shortest path which enables drivers to quickly and effectively collect the traf'c information. An impressive result is that the driver can compute/update their shortest path result and also gives alternative paths with the traffic count. Our experimental study shows that it is robust to various parameters and it offers relatively fast query response time (at client side), for online shortest path problem.

Keywords ' Shortest path, Dijkstra's Algorithm, Traffic condition

1. INTRODUCTION

This paper involved in illustrating the best way to travel between two points and in doing so, the shortest path algorithm was created. Shortest Path problem aims at computing the shortest path based on traf'c circumstances and gives the best path and also alternative paths. This is very important in modern navigation systems as it can help to make sensible decisions. Dijkstra's Algorithm is a graph search algorithm that solves the single-source shortest path problem for a graph with nonnegative edge path costs, producing a shortest path tree. This algorithm is often used in routing and other network related protocols. For a given source vertex (node) in the graph, the algorithm finds the finding costs of shortest paths from a single vertex to a single destination vertex by stopping the algorithm once the shortest path to the destination vertex has been determined. For example, if the vertices of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A large amount of work has been done on finding shortest paths through abstract. Dijkstra's algorithm is a Shortest Path Finding Algorithm which is applicable on a Graph which is Directed and got the Edges weighted with non-negative weights. If we have an undirected graph with edges unweighted, we can solve the problem with the implementation of Breadth First Search (BFS) algorithm. As we know we are unable to use BFS algorithm in case of a weighted and directed graph, but we can modify our algorithm of BFS in such a way that we can handle the above stated issues (weights and direction). We will later know that Dijkstra's algorithm is asymptotically the fastest known single-source shortest-path algorithm for arbitrary directed graphs with unbounded nonnegative weights. These are the motivations that will help us to know further about the Dijkstra's algorithm.

2. RELATED WORK

The indoor navigational assistance for this type of users [1] presents additional challenges not faced by conventional guidance systems, due to the personal nature of the interactions. The algorithms are part of an overall Indoor Navigation Model that is used to provide assistance and guidance in unfamiliar indoor environments. Path planning uses the Dijkstra's shortest path algorithms, to operate on an "Intelligent Map' that is based on a new data structure Termed "cactus tree" which is predicated on the relationships between the different objects that represent an indoor environment. This research explores the potential to design an application for the visually impaired even when to- date 'positioning and tracking' system cannot offer reliable position information that highly required by this type of application. The best-path problem for public transportation systems [3], we found that the nature of transfer is that it requires extra costs from an edge to its adjacent edge. So, we use the direct/indirect adjacent edges weighted directed graph as a public transportation data model and improve the storage of an adjacency matrix. We introduce the space storage structure in order to store the scattered information of transfer in indirect adjacent edges lists. Thus, we solve the problem of complex network graphs' storage and design a new shortest path algorithm to solve transit problem based on the data model. Algorithm analysis exhibits that the data model and the algorithm we propose are prior to a simple graph based on the Dijkstra's algorithm in terms of time and space. Today, the increased traffic and complex modern road network have made finding a good route [4] from one location to another a non-trivial task. Many search algorithms have been proposed to solve the problem, and the most well-known being Dijkstra's algorithm, Johnson's algorithm. While these algorithms are effective for path finding, they are wasteful in terms of computation. In this paper, we present a study to examine both uninformed search and heuristic search based on some major cities and towns. Efficient usage of routing algorithms [16] can significantly reduce travelling distance and transportation costs as well. Usage of the shortest-path algorithm in this case Dijkstra's algorithm for inner transportation optimization in warehouses. The model integrates data such as: 2D graph of warehouse layout, its 3D extension, historical data, and ABC analysis and business process model. The prototype of proposed application is tested with sample data and by simulating different working conditions.

3.  PROPOSED SYSTEM

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. Thus, it develops a new framework called towards online shortest path which enables drivers to quickly and effectively collect the traf'c information which is represented through object as traffic. It also gives shortest path as well as alternative path with traffic count. We can also add, edit and delete the nodes and edges in the graph.

3.1 Algorithm Use

All the above-mentioned techniques are put together for computing the shortest path. The algorithm is run at the client side.  

1. Dijkstra's Algorithm:

Let the node at which we are starting be called the initial node. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step. For the first iteration, the current intersection will be the starting point and the distance to it will be zero. For subsequent iterations (after the first), the current intersection will be the closest unvisited intersection to the starting point'this will be easy to find. From the current intersection, update the distance to every unvisited intersection that is directly connected to it. This is done by determining the sum of the distance between an unvisited intersection and the value of the current intersection and relabeling the unvisited intersection with this value if it is less than its current value. In effect, the intersection is relabeled if the path to it through the current intersection is shorter than the previously known paths. To facilitate shortest path identification, in pencil, mark the road with an arrow pointing to the relabeled intersection if you label/relabel it, and erase all others pointing to it. After you have updated the distances to each neighboring intersection, mark the current intersection as visited and select the unvisited intersection with lowest distance (from the starting point) or the lowest label'as the current intersection. Nodes marked as visited are labelled with the shortest path from the starting point to it and will not be revisited or returned to.

4. EXPERIMENTAL RESULT

In this section, we conduct an experiment to compare the paths between the nodes. In that paths, the shortest path was done by using dijkstra's algorithm. Here the shortest path it means low cost was found by the shortest path algorithm. We have also added some object as a traffic element between the routes. It also shows alternative paths with traffic count on the way. We can also add, edit and delete the nodes and edges in the graph. With the use of java software, the result was shown in the report. We have got successful result. The experiment was successfully complete. The result of this project finding the shortest path for a single source to all pairs of vertices by using the Dijkstra's Algorithm. It gives the cheapest cost and its implementation is easy.

Sr.no System Nodes Time

(ms) Alternative

Path Traffic

Count

1. Existing

System 15 136 No No

2. Proposed

System 15 117 Yes Yes

Table 4.1 Shows comparison between existing and proposed model

 Figure 4.1Comparison of number of node and time taken.

Figure 4.2 Shows Alternative path with Traffic count

5. CONCULSION

In this paper studies online shortest path computation; the shortest path result is computed/updated based on the traffic circumstances. It carefully analyzes the existing work and discuss their inapplicability to the problem. We have proposed a practical algorithm for the shortest path problem in transportation networks. The proposed algorithm can limit the search in a sub-graph based on the given nodes of the distance between the two nodes. As a result, the calculation for the shortest path has been simplified and also gives alternative path with traffic count. Experimental results on a real-world road network reflect the potential characteristic of the proposed algorithm in comparison to the existing works.

References

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[2] Reza Soltan Aghaei, M.; Zukarnain, Z.A.; Mamat, A.; Zainuddin, H., "A Hybrid Algorithm for the Shortest-Path Problem in the Graph, "Advanced Computer Theory and Engineering, 2008. ICACTE '08. International Conference on, vol., no., pp.251, 255, 20-22 Dec. 2008.

[3] Hongmei Wang; Ming Hu; Wei Xiao, "A new public transportation data model and shortest-path algorithms," Informatics in Control, Automation and Robotics (CAR), 2010 2nd International Asia Conference on , vol.1, no., pp.456,459, 6-7 March 2010.

[4] F. B. Zhan and C. E. Noon, Shortest Path Algorithms: An Evaluation Using Real Road Networks. Transportation Science. Vol.32, pp.65-73, February 1, 1998.

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[11] Wenyan Zhou; Qizhi Qiu; Peng Luo; Pei Fang, "An improved shortest path algorithm based on orientation rectangle for restricted searching area," Computer Supported Cooperative Work in Design (CSCWD), 2013 IEEE 17th International Conference on ,vol., no.,pp.692,697, 27-29 June

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[13] Tieyuan Yin; Jianyong Yang, "Notice of RetractionDynamic application of the path selection in the road," Software Engineering and Service Sciences (ICSESS), 2010 IEEE International Conference on , vol., no., pp.249,252, 16-18 July 2010.

[14] Yin Chao; Wang Hongxia, "Developed Dijkstra shortest path search algorithm and simulation," Computer Design and Applications (ICCDA), 2010 International Conference on, vol.1, no., pp.V1-116, V1-119, 25-27 June 2010.

[15] Zhang Fuhao; Liu Jiping, "An Algorithm of Shortest Path Based on Dijkstra for Huge Data," Fuzzy Systems and Knowledge Discovery, 2009. FSKD '09. Sixth International Conference on, vol.4, no., pp.244, 247, 14-16 Aug. 2009.

[16] Ji-xian Xiao; Fang-Ling Lu, "An improvement of the shortest path algorithm based on Dijkstra algorithm," Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on, vol.2, no., pp.383, 385, 26-28 Feb. 2010.

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 [18] IEEE Transactions on Knowledge and Data Engineering, Vol. 26, No. 4, April 2014,' Towards Online Shortest Path Computation' Leong Hou U, Hong Jun Zhao, Man Lung Yiu, Yuhong Li, and Zhiguo Gong.  

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