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# Assignment 3 — Undirected Graphs

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CSC 349: Design and Analysis of Algorithms
Assignment 3 — Undirected Graphs
Graphs allow us to mathematically and computationally model and explore the relationships that occur in
real world situations. One possible relationship that we might be interested in is some form of conflict between
two entities. For example, vertices could represent university classes, where two vertices are connected by an
edge if those classes’ times overlap.
Deliverables:
GitHub Classroom: https://classroom.github.com/a/TbnVCgQo
Required Files: compile.sh, run.sh
Optional Files: *.py, *.java, *.clj, *.kt, *.js, *.sh
Part 1: Graph Colorings
A vertex coloring is an assignment of colors, one color to each vertex, such that no two adjacent vertices
have the same color. If a graph can be colored using k colors, it is said to be k-colorable. In the situation
described above, where edges connect classes with conflicting times, a coloring could represent classroom
assignments such that no two classes are in the same classroom at the same time. For example:
v0
v1
v3
v2
v4
v5
The above graph can be colored using two colors, and it is said to be 2-colorable. For this special case of
k = 2, the 2-colorability of a graph can be computed in linear time (for k ≥ 3, finding valid colorings generally
becomes very difficult).
In your programming language of choice per Assignment 1, implement an algorithm to determine whether or
not a given graph is 2-colorable. To help you get started, note the following observations:
· In order to establish the 2-colorability of a graph, every vertex must be assigned exactly one color.
· Thus, every vertex should be explored exactly once by the coloring algorithm.
· The choice of cyan and magenta in the example above was entirely arbitrary; any two colors would do.
· Moreover, the choice of which group of vertices was colored cyan was also arbitrary: the assigned colors
could be swapped, and the coloring would remain valid.
· The colors assigned within one component cannot affect the colors assigned within any other component.
However, if any one component is not 2-colorable, the entire graph is not 2-colorable.
Each input graph will be provided as an edge list: each edge in the graph will be represented by a commaseparated pair of vertex identifiers, indicating an edge from the first vertex to the second.
You may assume that vertex identifiers are contiguous natural numbers — they begin at 0, and there will be
no “gaps” in the identifiers used. You may also assume that the graph will be simple and will not contain
any isolated vertices.
1 of 2
CSC 349: Design and Analysis of Algorithms
Fall 2019
Assignment 3 — Undirected Graphs
Due: Monday, October 14th
For example, the above graph could be represented as:
0, 1
1, 2
2, 3
3, 0
4, 5
Your program must accept as a command line argument the name of a file containing an edge list as described
above, then print to stdout the result of the attempted 2-coloring according to the following format:
· Vertices assigned the same color within the same component appear on a single comma-separated line.
· Vertices assigned different colors appear on different lines. Vertices in different components appear on
different lines, even if they are assigned the same color.
· Each line’s vertices must be sorted in ascending order. Note that vertex identifiers are integers, not
strings. The lines themselves must be sorted in ascending order using their smallest vertex identifiers.
For example:
>\$ ./compile.sh
>\$ ./run.sh in1.txt
Is 2-colorable:
0, 2
1, 3
4
5
Your program will be tested using diff, so its printed output must match exactly.
Part 2: Submission
The following items must be demonstrated in lab on the day of the deadline:
· Pseudocode for an efficient algorithm to 2-color simple graphs.
· Analysis of complexity for the pseudocode.
The following files are required and must be pushed to your GitHub Classroom repository by the deadline:
· compile.sh — A Bash script to compile your submission (even if it does nothing), as specified.
· run.sh — A Bash script to run your submission, as specified.
The following files are optional:
· *.py, *.java, *.clj, *.kt, *.js, *.sh — The Python, Java, Clojure, Kotlin, Node.js, or Bash source
code files of a working program to 2-color simple graphs, as specified.
Any files other than these will be ignored.