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• Subject area(s): Engineering
• Published on: 7th September 2019
• File format: Text
• Number of pages: 2

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Towards Online Shortest Path using

Dijkstra Algorithm

Neha Makariye                                               Deepa Deshpande

Abstract- Shortest Path problems plays an important role in applications of road network such as handling city emergency and driver guiding system. The concepts of network analysis with traffic issues are explored. The traffic condition among a city changes periodically and there are usually large amounts of requests occur, it needs to solve quickly. By using the Dijkstra’s Algorithm, the above problems can be solved through shortest paths. The main objective is the low cost of the implementation. The shortest path and the best path is computed based on the problem of trafﬁc circumstances shortest path. This plays an important role in modern navigation systems as it can help to make sensible and time saving decisions. Thus, it develops a new framework called towards online shortest path which enables drivers to quickly and effectively collect the trafﬁc information. An impressive result is that the driver can get their shortest path result and also gives alternative paths for the same route with the traffic count. Our experimental study shows that it is robust to various parameters and it offers relatively fast query response time, for online shortest path problem.

Keywords — Dijkstra’s Algorithm, Shortest path, Traffic condition

1. INTRODUCTION

This paper involved in showing the best way to travel from one point to another and in doing so, the shortest path algorithm was created. The shortest path and the alternative path is computed based on the problem of trafﬁc circumstances shortest path and gives the traffic count. This plays an important role in modern navigation systems as it can help to make sensible and time saving decisions.  To solves the shortest path problem of single-source for a graph with nonnegative edge path costs, gives shortest path tree, Dijkstra‘s Algorithm is used. This algorithm is mostly used in routing and other network connected protocols. For a given source vertex (node) in the graph, the algorithm finds the finding costs of shortest paths from a single node to a single destination node, once the shortest path to the destination node has been determined the algorithm is then stopped. For example, if the edges represent driving distances between pairs of cities connected by a direct road and nodes of the graph represent cities, Dijkstra\'s algorithm can be used to find the shortest path between one city to other cities. Through abstract large number of work is done on finding shortest paths. Dijkstra‘s algorithm is a shortest path finding algorithm which can be apply on a graph which is directed and got the edges with non-negative weights. If we implement Breadth First Search (BFS) algorithm, we can solve the problem of undirected graph with edges unweighted or with negative weight. We will later know that with unbounded nonnegative weights, Dijkstra‘s algorithm is asymptotically the fastest known shortest-path algorithm for arbitrary directed graphs. These are the basic things that will help us to know further about the Dijkstra‘s algorithm.

2. RELATED WORK

The navigational assistance for this type of users presents additional challenges not faced by conventional guidance systems, due to the personal nature of the interactions [2]. The algorithms are part of an overall Indoor Navigation Model that is used to provide assistance and guidance in unfamiliar indoor environments. To operate on an \"Intelligent Map” path planning uses the Dijkstra\'s shortest path algorithms, 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. The potential needed to design an application for the visually impaired, when to- date \'positioning and tracking\' system cannot offer proper position information that highly required by this type of application as this research finds. We found that the nature of transfer is that it requires extra costs from an edge to its adjacent edge this is the best-path problem for public transportation systems [3]. In order to store the scattered information related to transfer in indirect adjacent edges lists, we introduce the space storage structure. Thus, it solves the issue of complex network graphs storage and to solve transit issue based on the data model so it designs a new shortest path algorithm. We propose a prior to simple graph based on the Dijkstra\'s algorithm in terms of time and space as algorithm analysis exhibits. The complex modern road network has made finding a better route [4] from one location to another location by a non-trivial task, as now a day there is increased in traffic. There are many search algorithms that have been proposed to solve the problem of shortest path, and the most well-known algorithm are Dijkstra\'s algorithm and Johnson\'s algorithm. In this paper, we present a study to examine both uninformed search and heuristic search based on some major cities and towns. To significantly reduce travelling distance and transportation costs, efficient usage of routing algorithms is used. The prototype of proposed application is tested with sample data and by simulating different working and traffic conditions.

3. PROPOSED SYSTEM

Shortest Path problems plays an important role in applications of road network such as handling city emergency and driver guiding system. Basic concepts of network analysis with traffic problem are explored. The time to time changes in traffic condition among a city and there are usually large number of requests occur, it needs to find the solution quickly. The above problems can be solving 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 trafﬁc information. An impressive result is that the driver can get their shortest path result and also gives alternative paths for the same route with the traffic count.

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:

Dijkstra\'s Algorithm is to find the shortest path between two cities on a map, a starting point and a destination. Let start with node called the initial node. To improve them step by step Dijkstra\'s algorithm will assign some initial distance values. For the first iteration, the distance to it will be zero and the current intersection will be the starting point. For subsequent iterations, the current intersection will be the closest unvisited intersection to the starting point—this will be easy to find. Update the distance to every unvisited intersection that is directly connected to it, from the current intersection. This is done by calculating the sum of the distance between a value of the current intersection and unvisited intersection and the and relabeling the unvisited intersection with this value, if it is less than its current value. In effect to determine, the intersection is relabeled if the path through the current intersection is shorter than the previously paths. To identify the shortest path, take a pencil and 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 or the lowest label, as the current intersection. Continue this process of updating the neighboring intersections with the shortest distances and can trace your way back, following the arrows in reverse. The marked nodes will be as visited nodes, 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 of proposed and existing system. In that paths, the shortest path is find 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. It also shows the three-alternative path for one route and its traffic count of each alternative path. We have got successful result. The experiment was successfully complete. 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 study, online shortest path computation; the shortest path result is computed based on the traffic condition. It carefully analyzes the existing work and discuss their inexplicabilities to the problem. To address the problem, it suggests a promising architecture that is a practical algorithm for the shortest path problem in travelling networks. As a result, this first identify an important feature of 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

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

[2] Hua Wu; Marshall, A.; Yu, W., \"Path Planning and Following Algorithms in an Indoor Navigation Model for Visually Impaired,\" Internet Monitoring and Protection, 2007. ICIMP 2007. Second International Conference on, Vol., No., pp.38, 38, 1-5 July 2007.

[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.

[5] Abbas, M.A.; Chumachenko, S.V.; Hahanova, A.V.; Gorobets, A.A.; Priymak, A., \"Models for quality analysis of computer structures,\" East-West Design & Test Symposium, 2013, Vol., No., pp.1, 6, 27-30 Sept. 2013.

[6] A.V. Goldberg and R.F.F. Werneck, “Computing Point-to-Point Shortest         Paths from External Memory,”Proc. SIAM Workshop Algorithms Eng. and Experimentation and the Workshop Analytic Algorithmics and          Combinatorics (ALENEX/ANALCO), pp. 26-40, 2005.

[7] “Network-Based Generator of Moving Objects,” http://iapg. jade-hs.de/personen/brinkhoff/generator/, 2014.