A tram also known as tramcar; and in North America known as streetcar, trolley or trolley car , is a rail vehicle which runs on tracks along public urban streets called street running [1] [7].

### VSLAM and Navigation System of Unmanned Ground Vehicle Based on RGB-D Camera

Tram network is presently in existence in Melbourne University, Australia. The Melbourne tramway network is a major form of public transport in Melbourne, the capital city of the state of Victoria, Australia [2]. As at May , the network consisted of kilometres of track, trams, 25 routes, and tram stops. It is the largest urban tramway network in the world, ahead of the networks in St.

Petersburg km , Berlin km , Moscow km and Vienna km [2] [6]. Members of the university community have to travel from one point to another on campus for different reasons, ranging from attending lectures to attending meetings. In order to travel and arrive at destinations in good times, movement path has to be chosen wisely.

This is an example of shortest path problem and the weight will be the time cost. Certainly different routes will involve different stations and pathways [8] [9].

For this paper, we assume that the tram network will cover only the following spots on covenant university campus, which represent the stations, in Table 1. Table 2 shows the initial distance between two given spots stations on campus. Figure 1 , on the other hand, shows the directed weighted graph showing the network of the proposed rail paths, with the edges as the initial distance between two given stations. The network, formed using Table 2 , is to be optimized, by finding the shortest path from station A Canaan land entrance gate , which is our starting node, to station U Electrical Engineering department , which is our target node.

- Dijkstra's algorithm;
- Combining Hierarchical and Goal-Directed Speed-Up Techniques for Dijkstra’s Algorithm.
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- Approximate Shortest Path and Distance Queries in Networks.
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Dijkstra algorithm is applied on the network in Figure 1 to find the shortest distance from node A. Table 1. Proposed rail stations on camp. Figure 1. Directed graph showing the distances between the nodes. The main advantage of this work is the fact that a simple algorithm, such as Dijkstra algorithm, can be applied, with some assumptions, to estimate the shortest part of a proposed tramway in a potential world class university.

Tramway transit system is very new in universities in sub-Saharan Africa countries. Tram system will soon be the transit mode of choice among many sub-Saharan Universities of lower to medium population density. Some of the advantages of this would be lower cost and greater flexibility, reduction in carbon dioxide emission and convenience, especially during rainy season. Also, the following are other benefits of this transportation system; extension of rail network to areas currently not served by campus shuttle cars, reduction in cost of transportation within the covenant university, reduction in carbon monoxide in the air, making the university cleaner and always quite, making the university accessible and socially vibrant [2] [6] [9].

He was known for his many essays on programming. The object of this paper therefore, is to present an optimisation model [3] [9] [10] , which deals with the selection of the routes on which services will be offered using TRAM system in Covenant University [6] [11] [12]. This study exposes the need for a Tram transportation system on campus with expanded rail network to meet the growing needs of the university as regards mobility.

## Dijkstra's algorithm - Wikipedia

It is also intended to know how to move from one point to another in a potential world class university, in order to save time and reduce cost [13] [14]. This is a single source shortest path problem [10] [11].

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For IEEE to continue sending you helpful information on our products and services, please consent to our updated Privacy Policy. Email Address. Sign In. Access provided by: anon Sign Out. Research of shortest path algorithm based on the data structure Abstract: The shortest path problem based on the data structure has become one of the hot research topics in graph theory.

Concieved by Edsger Dijkstra. Condition: Both directed and undirected graphs All edges must have nonnegative weights Graph must be connected.

## Approximate Shortest Path and Distance Queries in Networks

Algorithm: Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.

Mark all nodes unvisited. Set the initial node as current. Create a set of the unvisited nodes called the unvisited set consisting of all the nodes. For the current node, consider all of its unvisited neighbors and calculate their tentative distances. When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.

If the destination node has been marked visited when planning a route between two specific nodes or if the smallest tentative distance among the nodes in the unvisited set is infinity when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes , then stop.