Description
Submission:
• DGraph.java – Class representing a directed graph.
• PA11Main.java – Class to perform different algorithms to solve the traveling salesman
problem.
• README.md – Results of timing experiments that compare your improved algorithm
to the required algorithms for the input file big11.mtx and describes why the algorithms
have relative performance differences. Note we have already provided this blank file in
your eclipse project. You just need to edit it.
Overview
This assignment has multiple goals:
• To practice new algorithmic patterns: recursive backtracking and heuristic
• To work with a new data structure: graphs
• Decomposition: using multiple interacting classes to achieve a larger goal
• Continue the discussion of performance analysis that we have started this semester
The Traveling Salesperson problem asks what is the shortest trip through a sequence of locations and back to the beginning while only visiting each location once. The distances between
locations are the input to the problem. These distances can be represented as weights on edges
in a graph.
The Traveling Salesperson problem is a famous problem in computer science. It is an
example of an NP-Complete problem. There are a significant number of NP-Complete problems that can all be converted to each other (see here). Some examples: vehicle routing, circuit
design, and robot navigation.
Assignment
You will be solving the traveling salesperson problem using three different ways: recursive
backtracking, heuristic, and your own approach.
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To use the program, someone will need to put two command line arguments into your
program:
PathTo/infile.mtx [HEURISTIC, BACKTRACK, MINE, TIME]
The input files are in the same format as the matrix market format used by the SuiteSparse
Matrix Collection. More importantly, see this link for a description of the .mtx format. You
can write code similar to this link to read in the .mtx format. Here is an example input file:
%%MatrixMarket matrix coordinate real general
3 3 6
1 2 1.0
2 1 2.0
1 3 3.0
3 1 4.0
2 3 5.0
3 2 6.0
Example output to standard out is provided in the PublicTestCases/ for HEURISTIC and
BACKTRACK. Here is the output for the above input file and the HEURISTIC command:
cost = 10.0, visitOrder = [1, 2, 3]
You will be running your own algorithm with the MINE command. The output for time
is shown later in this spec.
This assignment is broken down into parts. You could use iterative development to tackle
each part individually: finish reading in the .mtx file into a graph data structure, the heuristic
part of the assignment, and the recursive backtracking, mine, and time commands.
There is pseudocode in this spec. As with the last assignment, it is crucial that you understand how the pseudocode works, what it is doing, and why it is doing what it is doing
before actually writing the code for it, or else you will be lost. Not to mention it will be very
difficult to improve upon an algorithm that you do not understand well.
Part One: DGraph
Before you can run algorithms on a graph, you need a graph. The first part of this assignment
will be reading in a .mtx file and converting the file into a code representation of a graph.
You will need to fill in certain methods and fields in the DGraph.java file. This file exports a
class called DGraph. This class will store all necessary information about the graph. See the
DGraph.java file in the starter code for a list of methods to fill in. You should extensively test
this class before moving on. Lingering bugs in the DGraph class will make debugging the
later part of the assignment nearly impossible.
With your DGraph class working, it is time to write code to read in a .mtx file and store it
properly into your DGraph class. This should be done in PA11Main.java. File format descriptions are listed above in the ’Assignment’ section. Additionally, we have provided testcases
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and their corresponding .dot files. These files will be a great testing tool. There are many
graph visualizers on the web that accept a .dot file and show you a visualization of the graph.
For instance, check out the example.mtx file and then use an online .dot visualizer to view
the example.mtx.dot file as a visual graph to understand this file format. The starter code we
gave you has methods that will build the dot file as a string for you. I just used this site which
happened to be the first google result for me.
Part Two: Heuristic
Below is the pseudocode we expect you to follow for the HEURISTIC command. If you have
ideas on how to improve it, great, save those for the MINE command. Note now would be a
good time to review Trip.java which was given as part of the starter code.
create a trip
choose city 1 first, call it the current city
for k=2 to numNodes inclusive
for each neighbor of the current city
find the neighbor that is available AND the closest to the current city
choose the closest city that is available for the trip
call that closest city the current city
Part Three: Recursive Backtracking
We will make the decisions starting with node 1 and continuing through the nodes in order.
Everytime a node is chosen, that choice will be checked before recursing to do some pruning.
We cannot stop at the first node we find, because it is possible that paths through other nodes
will cost less.
create a trip
choose city 1 first
call backtrackingFunction on the trip
backtrackingFunction( graph data structure, current trip so far,
min trip previously found )
if all nodes are in trip then
process the current trip:
does it have less cost than min trip?
if so then modify min trip previously found (hint: copyOtherIntoSelf())
return
if trip so far has less cost than the min trip previously found
for each city x of the cities left
choose x next
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backtrackingFunction( graph data structure, updated trip,
min trip previously found )
unchoose x
Part Four: Your own approach
You will also implement the command MINE that executes your own faster algorithm for
performing the traveling salesperson problem. The code you submit should be able to execute
the MINE command. For your own approach you can choose to do one of the following:
• improve upon the heuristic approach while not resorting to a trivial solution like just
listing all of the nodes in order
• improve upon the recursive backtracking approach by putting in more pruning and
then show this is faster than the suggested recursive backtracking approach
Part Five: Timing all of the approaches
Using code similar to the following, you will have a TIME command that times all of the
algorithms.
long startTime = System.nanoTime();
trip = heuristic(graph);
long endTime = System.nanoTime();
long duration = (endTime – startTime) / 1000000;
System.out.println(“heuristic: cost = ” + trip.tripCost(graph) + “, ” + duration +
” milliseconds”);
The output for the TIME command will look as follows:
heuristic: cost = 935.3299999999999, 0 milliseconds
mine: cost = 935.3299999999999, 0 milliseconds
backtrack: cost = 835.8799999999999, 5 milliseconds
None of the grading test cases call TIME, because each time you run the program even on
the same input and on the same machine there will be some time variance. Because of that
you will probably want to run the timings about 5 times before drawing any conclusions.
A good test is to run the TIME command on your machine for big11.mtx. It takes around
a minute for the recursive backtracking algorithm on a 3 year old Mac.
Error Handling
All of the inputs will be correctly formed for this assignment.
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Hints
• The node IDs go from 1 to the number of nodes inclusive because the sparse matrix
market file format (.mtx) stores node IDs starting at 1 instead of 0.
• We are providing a Trip class that keeps track of a Trip. Read its usage instructions.
• Start early!
• Test the various pieces of your program very well. If you do not ensure that each piece
works perfectly, you will find very difficult to detect issues with the whole. Use the
debugger and/or various print statements.
Grading Criteria
We are providing testcases for this PA. We will also have our own private grading testcases.
We encourage you to write your own JUnit testcases to ensure your classes work properly,
but we will not be collecting or grading these test files.
Your grade will consist of similar style and code clarity points we have looked for in earlier
assignments.
Write your own code. We will be using a tool that finds overly similar code. Do not look at
other students’ code. Do not let other students look at your code or talk in detail about how
to solve this programming project. Do not use online resources that have solved the same or
similar problems. It is okay to look up, ”How do I do X in Java”, where X is indexing into an
array, splitting a string, or something like that. It is not okay to look up, ”How do I solve {a
programming assignment from CSc210}” and copy someone else’s hard work in coming up
with a working algorithm.
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