JAVA BASED VISUALIZATION AND ANIMATION FOR TEACHING THE DIJKSTRA SHORTEST PATH ALGORITHM IN TRANSPORTATION NETWORKS

International Journal of Software Engineering & Applications (IJSEA), Vol.7, No.3, May 2016
DOI: 10.5121/ijsea.2016.7302 11
JAVA BASED VISUALIZATION AND ANIMATION FOR
TEACHING THE DIJKSTRA SHORTEST PATH
ALGORITHM IN TRANSPORTATION NETWORKS
Ivan Makohon1
, Duc T. Nguyen2
, Masha Sosonkina3
, Yuzhong Shen4
and Manwo Ng5
1
Graduate Student, Department of Modeling, Simulation & Visualization Engineering
(MSVE), Old Dominion University (ODU), Norfolk, Virginia
2
Professor, Civil & Environmental Engineering (CEE) Department, ODU, Norfolk,
Virginia
3
Professor, Department of MSVE,ODU, Norfolk, Virginia
4
Associate Professor, Department of MSVE, ODU, Norfolk, Virginia
5
Assistant Professor, Department of Information Technology and Decision, ODU,
Norfolk, Virginia
ABSTRACT
Shortest path (SP) algorithms, such as the popular Dijkstra algorithm has been considered as the “basic
building blocks” for many advanced transportation network models. Dijkstra algorithm will find the
shortest time (ST) and the corresponding SP to travel from a source node to a destination node.
Applications of SP algorithms include real-time GPS and the Frank-Wolfe network equilibrium.
For transportation engineering students, the Dijkstra algorithm is not easily understood. This paper
discusses the design and development of a software that will help the students to fully understand the key
components involved in the Dijkstra SP algorithm. The software presents an intuitive interface for
generating transportation network nodes/links, and how the SP can be updated in each iteration. The
software provides multiple visual representations of colour mapping and tabular display. The software can
be executed in each single step or in continuous run, making it easy for students to understand the Dijkstra
algorithm. Voice narratives in different languages (English, Chinese and Spanish) are available.A demo
video of the Dijkstra Algorithm’s animation and result can be viewed online from any web browser using
the website: http://www.lions.odu.edu/~imako001/dijkstra/demo/index.html.
KEYWORDS
Transportation, Dijkstra Algorithm, Java, Visualization, Animation

12
1. INTRODUCTION
Finding the shortest time (ST), or the shortest distance (SD) and its corresponding shortest path
(SP) to travel from any i-th “source” node to any j-th “destination (or target)” node of a given
transportation network is an important, fundamental problem in transportation modelling.
Efficient SP algorithms, such as the Label Correction Algorithm (LCA) and its improved version
of Polynomial (or partitioned) LCA, forward Dijkstra, backward Dijkstra, Bi-directional Dijkstra,
A* algorithms have been developed, tested and well documented in the literatures [1-3].
Teaching the SP algorithms (such as the Dijkstra algorithm), however, can be a
difficult/challenging task!
While some teaching information/lecture/tool/animation for Dijkstra algorithms have
existed/appeared in the literatures [4-6], none seems to be suitable/appropriate for our students’
learning environments, due to the lack of one (or more) of the following desirable
features/capabilities:
1. The developed software tool should be user friendly (easy to use).
2. Graphical/colourful animation should be extensively used to display equations, and/or
intermediate/final output results.
3. Clear/attractive computer animated instructor’s voice should be incorporated in the
software tool.
4. The instructor’s voice for teaching materials can be in different/major languages
(English, Chinese, and Spanish).
5. User’s input data can be provided in either interactive mode, or in edited input data file
mode, or by graphical mode.
6. Options for partial (or intermediate) results and/or complete (final results) are available
for the user to select.
7. Options for displaying all detailed intermediate results in the first 1-2 iterations, and/or
directly show the final answers are available for users.
8. Users/learners can provide his/her own data, and compare his/her hand-calculated results
with the computer software’s generated results (in each step of the algorithm) for
enhancing/improving his/her learning abilities.
The remaining sections of this article is organized as follow. In section II, the basic forward
Dijkstra algorithm is summarized (for the readers’ convenience). Java language is adopted in this
work due to its powerful graphical and animated features. Special and useful features of the
developed Java software for teaching Dijkstra algorithm are high-lighted and demonstrated in
(including some computer screen captures) Section III. Conclusions are summarized/suggested in
Section IV.
2. SUMMARY OF THE BASIC FORWARD DIJKSTRA SHORTEST PATH
ALGORITHM
The basic forward Dijkstra algorithm is a graph search algorithm that solves for the shortest path,
time, or distance from any given source node to a destination node. The graph is
represented/stored within a 2-Dimentional NxN matrix where the rows and columns of the matrix
headers are represented as the nodes and the values within the matrix at a location (Aij) are the
link’s value (path, distance, or time value), refer to Figure 1. Figure 1 shows a simple 3 x 3

13
matrix where Node 1 Node 2 has a link value of 6, Node 1 Node 3 have a link value of 4,
and Node 2 Node 3 has a link value of 2
With any given N x N size matrix, the shortest path, time, or distance can be solved using the
basic forward Dijkstra shortest path algorithm. For example, we demonstrate and solve for a
sample 6 x 6 matrix (Figure 2) and graph (Figure 3) to find the shortest path, time, or distance
from Node 1 (source node) to Node 6 (destination node).
We demonstrate and use a simple (easy to use) bookkeeping (Figure 4) method while iterating
through the forward Dijkstra algorithm. Figure 4 shows the initial values for the Set s and Set s
prime. Set s is empty during initialization and is used to bookkeep nodes already visited. Set s
prime contains all the nodes during initialization and nodes are removed as they are visited. The
vector {d} bookkeeps the shortest path, time, or distance value and the vector {pred} bookkeeps
the predecessor nodes after each iteration within the Dijkstra algorithm.

14
During the first iteration, we set the source node to Node 1 and update Set s = {1} and Set s prime
= {2, 3, 4, 5, 6}. Note that Node 1 is removed from Set s prime and added to the Set s.
From Node 1, there are 2 outgoing links, Node 2 and Node 3 (Figure 3). We check the outgoing
Nodes (2 and 3) from Node 1 (Source Node) to determine if Vector [d] and [pred] need to be
updated with the shortest path, time or distance. This can be done referencing the values stored in
Vector d[2] and d[3]. Compare the stored Vector d[2] value to see if it’s greater-than the
computed value, which is the stored Vector d[1] plus the value at C13(link value between Node 1
and 3). Compare the stored Vector d[3] value to see if it’s greater-than the computed value,
which is the stored Vector d[1] plus C12(link value between Node 1 and 2). If the stored values
are greater-than the computed values then update the Vector d with the computed value. If not,
then no update is needed and the stored value remains the same.

15
In both of these cases, the stored values for d[2] and d[3] are infinity (∞) so the values in Vector
[d] and [pred] will need to be updated with the computed values (Figure 5). Figure 5 shows the
simple (easy to use) bookkeeping method and updates (if needed).
Once this calculation and update has taken place, we determine the smallest value among the
nodes in Set {s prime} and then we move the node to the Set {s}. Because Vector d[3] has the
smallest value among the nodes in Set {s prime}, we move Node 3 to Set {s} = { 1, 3 } and
remove it from Set {s prime} = { 2, 4, 5, 6 }. Now Node 3 becomes the next source node.
The Next iteration (k = 2), begins by checking the outgoing nodes from Node 3 (source node).
We check the outgoing Nodes (4 and 5) from Node 3 (Source Node) to determine if Vector [d]
and [pred] need to be updated with the shortest path, time or distance. This can be done
referencing the values stored in Vector d[4] and d[5]. Compare the stored Vector d[4] value to
see if it’s greater-than the computed value, which is the stored Vector d[3] plus the value at
C34(link value between Node 3 and 4). Compare the stored Vector d[5] value to see if it’s
greater-than the computed value, which is the stored Vector d[3] plus C35(link value between
Node 3 and 5). If the stored values are greater-than the computed values then update the Vector d
with the computed value. If not, then no update is needed and the stored value remains the same.

16
In both of these cases, the stored values for d[4] and d[5] are infinity (∞) so the values in Vector
[d] and [pred] will need to be updated with the computed values (Figure 6). Figure 6 shows the
simple (easy to use) bookkeeping method and updates (if needed).
smallest value among the nodes in Set {s prime}, we move Node 4 to Set {s} = { 1, 3, 4 } and
remove it from Set {s prime} = { 2, 5, 6 }. Now Node 4 becomes the next source node.
We check the outgoing Node 6 from Node 4 (Source Node) to determine if Vector [d] and [pred]
need to be updated with the shortest path, time or distance. This can be done referencing the
values stored in Vector d[6]. Compare the stored Vector d[4] value to see if it’s greater-than the
computed value, which is the stored Vector d[4] plus the value at C46(link value between Node 4
and 6). If the stored value is greater-than the computed value, then update the Vector d with the
computed value. If not, then no update is needed and the stored value remains the same.
In this case, the stored value for d[6] is infinity (∞) so the value in Vector [d] and [pred] will need
to be updated with the computed value (Figure 7). Figure 7 shows the simple (easy to use)
bookkeeping method and updates (if needed).
nodes in Set {s prime} and then we move the node to the Set {s}. Because Vector d[2] and d[5]
has the smallest value, 6 among the nodes in Set {s prime}, we arbitrarily select and move Node 2
to Set {s} = { 1, 3, 4, 2 } and remove it from Set {s prime} = { 5, 6 }. Now Node 2 becomes the
next source node. Note: we could do further research here to pick the better of the 2 choices
instead or arbitrarily selecting one.

17
see if it’s greater-than the computed value, which is the stored Vector d[2] plus the value at
C23(link value between Node 2 and 3). Compare the stored Vector d[4] value to see if it’s
greater-than the computed value, which is the stored Vector d[2] plus C24(link value between
Node 2 and 4). If the stored values are greater-than the computed values then update the Vector d
with the computed value. If not, then no update is needed and the stored value remains the same.
In both of these cases, the stored values for d[3] and d[4] are 4 and 5 respectively so the values
are not greater-than the computed values so no update is needed (Figure 8). Figure 8 shows the
simple (easy to use) bookkeeping method and updates (if needed). In this case, no update is
needed since the stored values are not greater-than the computed values.
smallest value among the nodes in Set {s prime}, we move Node 5 to Set {s} = { 1, 3, 4, 2, 5 }
and remove it from Set {s prime} = { 6 }. Now Node 5 becomes the next source node. Remark:
When determining the smallest value was a tie for Nodes 2 and 5 (see previous iteration), we
were better off to select and move Node 5 instead of arbitrarily selecting Node 2.
see if it’s greater-than the computed value, which is the stored Vector d[5] plus the value at C54
(link value between Node 5 and 4). Compare the stored Vector d[6] value to see if it’s greater-
than the computed value, which is the stored Vector d[5] plus C56(link value between Node 5 and
6). If the stored values are greater-than the computed values then update the Vector d with the
computed value. If not, then no update is needed and the stored value remains the same.
In both of these cases, the stored values for d[4] and d[6] are 5 and 12 respectively so the value
for d[4] is not greater-than the computed values so no update is needed (Figure 9). However, the
value for d[6] is greater-than the computed values in Vector [d] and [pred] will need to be
updated with the computed values (Figure 9). Figure 9 shows the simple (easy to use)

18
bookkeeping method and updates (if needed). In this case, one outgoing node is updated is
needed since the stored values is greater-than the computed values.
nodes in Set {s prime} and then we move the node to the Set {s}. Because Vector d[6] is the only
remaining node and is the destination node, we move Node 6 to Set {s} = { 1, 3, 4, 2, 5, 6 } and
remove it from Set {s prime} = { empty }. Now Node 6 becomes the next source node and is our
destination node. This completes the shortest path, time, or distance for solving for the basic
forward Dijkstra algorithm.

19
The updates for each iteration for Vector [d], Vector [pred], and Set {s} are displayed in Figures
10, 11, and 12, respectively. For each iteration, the highlighted circle (light blue circle) shows the
corresponding values being updated during that iteration.

3. JAVA COMPUTER A
FORWARD DIJKSTRA ALGORITHM
The previous section’s small-scale 6 x 6 Matrix [A] graph data will be used for the Java [7
computer animated software tool for teaching the
initialize and run the Java software. Once initialized, the application’s “Main Control” Graphical
User Interface (GUI) is displayed (Figure 13). This GUI controls the flow of the basic forward
Dijkstra algorithm teaching steps from start to finish and will provide detailed algorithm steps
while solving for the shortest path, time, or distance.
The users/learners will be able to input the matrix [A] data from several input options (input file,
manual input or randomly generated values) from the “Main Control” GUI. When an input
option is selected the user/learner will be able to modify the data within the “Matrix Editor” GUI.
The “Matrix Editor” GUI (Figure 14) allows the user/learner to change the size of
dimensions and modify the values before solving for the shortest path, time, or distance.
ANIMATED SOFTWARE TOOL FOR T
LGORITHM
scale 6 x 6 Matrix [A] graph data will be used for the Java [7
computer animated software tool for teaching the Dijkstra algorithm. The users/learner will
hm teaching steps from start to finish and will provide detailed algorithm steps
while solving for the shortest path, time, or distance.
r randomly generated values) from the “Main Control” GUI. When an input
The “Matrix Editor” GUI (Figure 14) allows the user/learner to change the size of the matrix [A]
20
TEACHING
scale 6 x 6 Matrix [A] graph data will be used for the Java [7-9]
Dijkstra algorithm. The users/learner will
hm teaching steps from start to finish and will provide detailed algorithm steps
r randomly generated values) from the “Main Control” GUI. When an input
the matrix [A]

21
After the Matrix data [A] is entered into the "Matrix Editor" and "Ok" is selected, the focus is
returned back to the "Main Control" GUI. The matrix data [A] is shown in to viewable formats,
the “Matrix Canvas”, "Data", and "Network Graph" views. Both views will be updated
accordingly throughout the steps in the basic forward Dijkstra Algorithm.
Once the matrix data [A] is inputted, the "Play" button is enabled. Once the user/learner selects
the "Play" button, the teaching of the basic forward Dijkstra Algorithm steps begins. The basic
forward Dijkstra Algorithm performs the algorithm steps against the matrix data [A], the matrix
data [A] is updated accordingly and displayed within the Views, and the algorithm steps is
lectured to the user/learner by a computer animated voice. The algorithm steps handled within the
Java software are as follows:
3.1. Step 0 – Initialization
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will handle the
matrix data if provided as a rectangular or tall matrix. The algorithm will add "dummy" rows (or
columns) with the maximum corresponding value within the matrix.
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will solve for
shortest path, time, or distance. The GUI will prompt an input dialog for the user/learning to
select what the source and destination nodes.
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will initialize the
data vectors and sets and set the source node (Figure 15).
3.2. Step 1 – Consider all Outgoing Edges from the Current Node
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will consider all
outgoing links from the current node and will determine if the stored Vector [d] values for the
outgoing nodes are greater-than the computed values of the previous node plus the link (edge)

22
values. If the stored Vector [d] value is greater-than the computed value then the Vector [d] value
is updated accordingly; otherwise, the value remains the same.
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will have animated
each step and provide detailed animated voice and text for each step (Figure 16).
3.3. Step 2 – Determine the Smallest “d” Value for each Node within Set
Sfinal`(Prime) and Move the Smallest Node to Set Sfinal
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will determine the
smallest value from the Set {s prime} and remove the smallest from Set {s prime} and add it to
Set {s}.

23
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will update the
current node as the source node for the next iteration (Figure 17).
3.4. Step 3 – Determine the Shortest Time and Path from the Source Node to the
Target Node
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will determine the
shortest path, time, or distance based on the outcome of the Dijkstra algorithms using the
bookkeeping of Vector [d], Vector [pred], Set {s}, Set {s prime}.
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will highlight the
shortest path (Figure 18).
The Java Computer Animation for Teaching the Forward Dijkstra Algorithm will display the final
results of the shortest path, time, or distance by highlighting the nodes and links from the source
to destination node.
4. CONCLUSIONS
In this article, the basic Dijkstra algorithm has been firstly summarized. Then, Java Computer
Animated Software Tool has been developed to enhance student’s learning. The developed Java
animated software has all the following desirable features/capabilities, such as:
1. The developed software tool should be user friendly (easy to use).
2. Graphical/colourful animation should be extensively used to display equations, and/or
intermediate/final output results.
3. Clear/attractive computer animated instructor’s voice should be incorporated in the
software tool.

24
4. The instructor’s voice for teaching materials can be in different/major languages
(English, Chinese, and Spanish).
5. User’s input data can be provided in either interactive mode, or in edited input data file
mode, or by graphical mode.
6. Options for partial (or intermediate) results and/or complete (final results) are available
for the user to select.
7. Options for displaying all detailed intermediate results in the first 1-2 iterations, and/or
directly show the final answers are available for users.
8. Users/learners can provide his/her own data, and compare his/her hand-calculated results
with the computer software’s generated results (in each step of the algorithm) for
enhancing/improving his/her learning abilities.
ACKNOWLEDGEMENTS
The partial support provided by the NSF grant # ACI-1440673 (ODU-RF Project # 100507-010)
to Duc T. Nguyen is gratefully acknowledged. The work of Sosonkina was supported in part by
the Air Force Office of Scientific Research under the AFOSR award FA9550-12-1-0476, and by
the National Science Foundation grants NSF/OCI---0941434, 0904782, 1047772.
REFERENCES
[1] Sheffi, Y., 1985. Urban Transportation Networks: Equilibrium Analysis with Mathematical
Programming Methods. Available free of charge at:
http://web.mit.edu/sheffi/www/urbanTransportation.html
[2] Lawson, G., Allen, S., Rose, G., Nguyen, D.T., Ng, M.W. “Parallel Label Correcting Algorithms for
Large-Scale Static and Dynamic Transportation Networks on Laptop Personal Computers”,
Transportation Research Board (TRB) 2013 Annual Meeting (Washington, D.C.; Jan. 13-17, 2013);
Session 844 Presentation # 13-2103 (Thursday, Jan. 17-2013; 10:15am-noon); Poster Presentation #
P13-6655.
[3] Paul Johnson III, Duc T. Nguyen, and Manwo Ng, “An Efficient Shortest Distance Decomposition
Algorithm for Large-Scale Transportation Network Problems”, TRB 2014 Annual Meeting
(Washington, D.C.; January 2014); Oral, and Poster Presentations.
[4] Dijkstra’s Shortest Path Algorithm.
http://www.cs.uah.edu/~rcoleman/CS221/Graphs/ShortestPath.html.
[5] Dijkstra Algorithm. http://students.ceid.upatras.gr/~papagel/project/kef5_7_1.htm.
[6] Dijkstra’s Algorithm.http://www3.cs.stonybrook.edu/~skiena/combinatorica/animations/dijkstra.html.
[7] Java Matrix Library (EJML).
Efficient http://code.google.com/p/efficient-java-matrix-library/wiki/EjmlManual.
[8] Google Translate Java. http://code.google.com/p/google-api-translate-java/.
[9] Java Platform Standard
Edition.http://www.oracle.com/technetwork/java/javase/downloads/index.htmllishers.

25
Authors
Ivan Makohon is a current Old Dominion University graduate student pursuing his Masters in Modeling
and Simulations. He has received his Bachelors of Science in Computer Science from Christopher
Newport University (CNU). He has been working as a contractor (and now, a civil servant) as a Senior
Software Engineer, and he is also a Private Pilot.
Duc T. Nguyen has received his B.S., M.S. and Ph.D. (Civil/Structural engineering) degrees from
Northeastern University (Boston), University of California (Berkeley), and the University of Iowa (Iowa
City), respectively. He has been a Civil Engineering faculty at Old Dominion University since 1985. He has
published 4 undergraduate/graduate textbooks. Over 160 research articles and nearly $ 4 million funded
projects have been generated by him. He has received Cray Research, NASA, ODU shining star, and Rufus
Tonelson Distinguished Faculty Awards. His name has been included in the ISIHighlyCited.com list of
most highly cited researchers in Engineering.
Masha Sosonkina has received her B.S. and M.S. degrees in Applied Mathematics from Kiev National
University in Ukraine, and a Ph.D. degree in Computer Science and Applications from Virginia Tech.
During 2003-2012, Dr. Sosonkina was a scientist at the US Department of Energy Ames Laboratory and an
adjunct faculty at Iowa State University. She is currently a professor of Modeling, Simulation and
Visualization Engineering at Old Dominion University. She has also been a visiting research scientist at the
Minnesota Supercomputing Institute, at CERFACS and INRIA French research centers. Her research
interests include high-performance computing, large-scale simulations, parallel numerical algorithms,
performance analysis, and adaptive algorithms.
Yuzhong Shen received his B.S. degree in Electrical Engineering from Fudan University, Shanghai, China,
M.S. degree in Computer Engineering from Mississippi State University, Starkville, Mississippi, and Ph.D.
degree in Electrical Engineering from the University of Delaware, Newark, Delaware. His research
interests include computer graphics, visualization, serious games, signal and image processing, and
modeling and simulation. Dr. Shen is currently an Associate Professor of the Department of Modeling,
Simulation, and Visualization Engineering and the Department of Electrical and Computer Engineering of
Old Dominion University. He is also affiliated with Virginia Modeling, Analysis, and Simulation Center
(VMASC). Dr. Shen is a Senior Member of IEEE.
Manwo Ng is currently an Assistant Professor of Maritime and Supply Chain Management at Old
Dominion University (ODU). He obtained his Ph.D. degree in Transportation from The University of Texas
at Austin. His research focuses on port operations, container shipping, and transportation network
modeling.

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