1) The document discusses algorithms for finding optimal bus routes between locations, including Dijkstra's algorithm and improvements made to address its limitations. 2) It analyzes shortest path algorithms based on graph theory, least transfers, and station matrices. An improved Dijkstra's algorithm is proposed to find shortest paths between any two nodes. 3) The results show the improved algorithm can determine the shortest distance and transfer routes between any four bus stations, demonstrating its accuracy and feasibility for route planning applications.

1. Advance Data Structures
FAKHRE ALAM
PRN No. 170831180004
Roll No. 179305004

2. Improved Dijkstra’s Algorithm and its Application in
Intelligent Transportation System

3. Today
discussion
1.Introduction.
2.Algorithms of Bus Exchange.
2.1. Shortest path finding algorithm based on the graph theory.
2.2.Optimal path finding algorithm based on the least transfer.
2.3. Optimal path finding algorithm based on the Station Matrix.
3. Improvement of Dijkstra's algorithm.
3.1. What is Dijkstra’s Algorithm.
3.2. Improved Dijkstra's algorithm
4. Result analysis of Dijkstra's algorithm
5. Summary.

4. Introduction
As China's economic society gains dramatic development,
the public transportation system is increasingly expanded
and passenger information is the thing. To resolve this
problem, it calls for a convenient and rapid bus line inquiry
system. We analyses the strength and weakness of existing
algorithms of bus exchange and the modified graph-based
Dijkstra’s algorithm. The improved Dijkstra’s algorithm will
be applied to the bus line inquiry system providing transfer
services for passengers.

5. Shortest path finding
algorithm based on
the graph theory.
1
Optimal path finding
algorithm based on the
least transfer.
2
Optimal path finding
algorithm based on
the Station Matrix.
3
Algorithms of Bus Exchange

6. 1. Shortest path finding algorithm based on the graph theory.
Shortest path finding algorithm
based on the graph theory is
processed as follows:
Abstract the entire public
transportation system as a road
network.
Find the shortest path from source
to target based on the classical
shortest path Dijkstra’s algorithm.
Convert the shortest path into bus
transfer scheme.

7. Strength and
Weakness of the
algorithm.
Strength
 Dijkstra's algorithm is of high efficiency when it is used to find
the shortest path between two short-distance nodes.
 The weight on the public transportation network graph can be set
flexibly.
Example
It can be set as the time consumed, including riding time and
waiting time or set as the distance. In this way, the path with
shorter time or distance will be found respectively.

8. Weakness
When N becomes larger, the
time complexity will be
increased accordingly,
causing the efficiency
unsatisfactory.
1
In the topological graph of
public transportation
network, the number of N
nodes is the same with the
number of bus stops.
2
It can only find the shortest
path from source to target.
That is, for a source node
and a destination node,
Dijkstra's algorithm will
provide only one optimal
path
3

9. 2. Optimal path finding algorithm based on the least transfer
Whenever to transfer during the trip, passengers may walk to the stop and wait for the bus, all these consuming
time and energy. Therefore, the transfer times should be fully considered in the optimal path finding algorithm.
Algorithm
 When finding paths from the source to the destination, passengers search n transfer schemes (if n is equal to
zero, it means no transfer).
 If n transfer schemes are not found, then search n+1 transfer schemes;
 If the destination can be reached by n transfer from the source, the path finding algorithm will end with n
transfer schemes provided.
 When n>0, the transfer scheme will be searched through recursive algorithm. If search results give more than
one scheme, time or distance should be taken into account to choose the optimal one .

10. Algorithm Step
Algorithmic steps.
 Find all bus stops within W meter(s) of the source.
 Find all paths where stops near the source are located.
 Find all bus stops within W meter(s) of the destination.
 Find all paths where stops near the destination are located.
 Mark all paths where stops near the destination are located as
feasible paths to the destination.
 Find all paths where stops near the source are located.
 If there are some paths marked as "feasible", the transfer
scheme will be established.
 If there are no paths marked as "feasible", mark all paths
where all stops on each path which stops near the destination
are located on are located as feasible paths to the destination.
 Repeat the step (6). If the transfer scheme is still not found,
repeat the step (8) until the transfer scheme is found.

11. Strength and weakness of this algorithm.
Strength
 The recursive method is adopted on the basis of non-stop path to find multiple transfer paths, easy to realize.
 This algorithm centres on the same elements between two path sets or stop sets.
 Multiple n-transfer paths can be provided, meeting users' demands for alternative paths. Since paths are
listed according to the order of increase in transfer times, the first few ones will be the preferred paths with
the least transfer.

12. Weakness
 The time complexity grows exponentially with the increase of
transfer times .
 It means that finding paths with multiple transfers will take a long
time so that users cannot obtain the transfer path as soon as
possible.
 This algorithm only considers the transfer times, neglecting the
time and distance.
Continue..

13. 3. Optimal path finding algorithm based on the station matrix
The transfer is an important indicator for users to consider in the public transportation
system. Based on this, a proper path can be found by building a transfer matrix of public
transportation network and using relevant algorithms. The transfer matrix shows the transfer
times for passengers to reach the destination from the source when they choose public
vehicles

14. Strength and weakness of this algorithm.
Strength
 No matter how the source and the destination are changed, the transfer matrix can be used universally without
repeated calculation, thus greatly increasing the efficiency of optimal path finding algorithm.
 Based on this algorithm, the path with the least transfer from the source to the destination can be visually
displayed, and passengers can also analyse the connectivity of the whole public transportation network.
 This algorithm takes the least transfer as its primary goal, meeting passengers' daily demands.

15. Weakness
 The urban transportation system and the bus stop remain changeable, the station-based transfer
matrix shall be updated regularly.
 Every time when the bus stop is changed, the matrix must re-calculate the transfer among all stops,
which costs a lot.
 With the increase in the number of bus stops, the station-based transfer matrix will become larger
and larger, reducing the efficiency in calculation, storage and acquisition of transfer matrix.

16. Improvement of Dijkstra's algorithm.

17. Dijkstra's algorithm, introduced by the
Dutch computer scientist , is a graph
searching algorithm.
Dijkstra’s algorithm is used to solve the
problems of finding the shortest path between
edge – weighted graphs in which all the weights
are non-negative
For a given source vertices it finds the lowest
cost(i.e. The shortest path) for every other
vertices
It can also be used to find the lowest cost for a particular
destination by the stopping the algorithm in between
What is Dijkstra’s
Algorithm

18. From the above algorithm analysis, it can be seen that the conventional Dijkstra's algorithm is used to
find the shortest path from a fixed source node to all other nodes in the graph G. While in the calculation
of the shortest path, we need to find the shortest path between any two nodes in the public transportation
network; therefore, it is essential to modify the conventional Dijkstra's algorithm.
Continue…..

19. Improved Dijkstra's algorithm
Dijkstra's algorithm is used to find the shortest path from a given source node to all other nodes in
the weighted graph. The shortest path between any two nodes in the weighted graph can be
calculated and it can be easily realized in computer. The revised algorithm is as follows:
Enter the source node s and the destination node d.
 Find a sub-node nearest to the source node from the V-set which contains all nodes in the
graph G.
 Traverse the length from this sub-node to the source node and determine the minimum value.
 Put this minimum value into W-set and this sub-node into S-set. Repeat the above steps until
V-set is empty or the destination node is found.

20. It is an example analysis of improved Dijkstra algorithm.
applied of improved Dijkstra algorithm to realize the shortest path between any two points. For example, the
shortest path of point 1 to 7 in Figure is 1 2 5 6 7, the shortest distance is 9. The shortest path of point 2 to 3 in
Figure is 2 1 3, the shortest distance is 7.

21. The shortest path and the shortest distance between each point in the weighted graph G are as
follows

22. Result analysis of Dijkstra's algorithm
The following indicates that there are 4 bus stations; the number represents the distance between each other：

23. The operation results are as follows
The above shows that the shortest distance between any two stations to reach and the transfer mode .

24. Real life applications of Dijkstra's Algorithm
1) It is used in Google Maps
2) It is used in finding Shortest Path.
3) It is used in geographical Maps
4) To find locations of Map which refers to vertices of graph.
5) Distance between the location refers to edges.
6) It is used in IP routing to find Open shortest Path First.
7) It is used in the telephone network.

25. Summary
Introduces several frequently-used optimal path finding algorithms and analyses their respective
strength and weakness. It also describes the conventional Dijkstra's algorithm and the modified
Dijkstra's algorithm. The modified Dijkstra's algorithm is with accuracy and feasibility proved.
Finally, I would like to extend my sincere gratitude to Guangdong Provincial Department of Science
and Technology for its funding by the project "Massive Key Technologies under the Cloud
Environment and their Applications in the Intelligent Transportation System" and colleagues for their
joint efforts.

26. References
 Improvement of Dijkstra’s Algorithm and Its Application in Route Planning
(http://ieeexplore.ieee.org/abstract/document/5569452/)
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 Liu N H. Music selection interface for car audio system using SOM with personal distance function[J].
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