The University of New South Wales - COMP9312 - 24T2 - Data
Analytics for Graphs
Assignment 1
Graph Storage and Graph Traversal
Summary
Submission Submit an electronic copy of all answers on Moodle
(only the last submission will be used).
Required
Files
A .pdf file is required. The file name should be
ass1_Zid.pdf
Deadline 9pm Friday 21 June (Sydney Time)
Marks 30 marks (15% toward your total mark for this
course)
Late penalty. 5% of max mark will be deducted for each additional day
(24hr) after the specified submission time and date. No submission is
accepted 5 days (120hr) after the deadline.
START OF QUESTIONS
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Figure 1
Figure 2
Figure 3
Q1. Required knowledge covered by Topic 1.1 (4 marks)
Please determine whether the following statements for the graph in
Figure 1 are TRUE or FALSE.
a. In some correct BFS traversal starting from H, M can be traversed
before N.
2024/6/5 15:03 COMP9312 24T2 Assignment 1
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b. In some correct DFS traversal starting from I, E can be traversed
before A.
c. In any correct DFS traversal starting from E, G must be traversed
after F.
d. In any correct BFS traversal starting from K, L must be traversed
after H.
e. In any correct BFS traversal starting from A, N must be traversed
before G.
f. In any correct DFS traversal starting from P, A must be traversed
before Q.
g. In some correct DFS traversal starting from M, Q can be traversed
after K.
h. In some correct BFS traversal starting from J, A can be traversed
after E.
Marking for Q1: 0.5 mark is given for each correct TRUE/FALSE
answer.
Q2. Required knowledge covered by Topic 1.1 (5 marks)
Consider the undirected graph in Figure 2 stored by the adjacency list.
For each vertex, the neighbors are arranged alphabetically (e.g., the
neighbor list of A is [B,E,P]). Describe an algorithm to compute all
connected components using the disjoint-set data structure. Show the
tree structure after each union operation.
Marking for Q2: Full marks are given if each intermediate disjoint-set
tree structure is correct.
Q3. Required knowledge covered by Topic 1.1 (5 marks)
Consider the directed graph in Figure 3 stored by the adjacency list.
The neighbors of each vertex are arranged alphabetically. Compute the
topological order of vertices in the graph. Show intermediate steps.
Marking for Q3: Full marks are given if the described process of each
vertex is correct and the order of vertices are correct.
Q4. Required knowledge covered by Topic 0 (6 marks)
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We consider an undirected, unweighted graph with n vertices and m
edges. Design a data structure to store the graph that can efficiently
support the following three operations:
1) Scanning all neighbours of a given vertex,
2) Inserting a new edge that does not exist in the original graph
3) Deleting a vertex from the graph, including all edges related to it.
Justify the time complexity of each operation and the space complexity
of the data structure.
Marking for Q4: Two factors are evaluated in marking: (1) How good is
your time complexity and space complexity; (2) Does your algorithm
match your time complexity. (3) Does your data structure match your
space complexity. Full marks are given if your time complexity is not
larger than our expected one and your algorithm corresponds with your
time complexity.
Q5. Required knowledge covered by Topic 1.1 (5 marks)
We consider an undirected, unweighted graph with n vertices and m
edges organized using an adjacency list. Design an algorithm to
determine whether there exists a cycle that contains the given query
vertex (i.e., the input is a vertex ID, and the result should be TRUE or
FALSE). Please write your code in pseudocode and justify the time
complexity of each subpart, as well as the total time complexity of your
algorithm.
Marking for Q5: Two factors are evaluated in marking: (1) How good is
your time complexity; (2) Does your algorithm match your time
complexity. Full marks are given if your time complexity is not larger
than our expected one and your algorithm corresponds with your time
complexity.
Q6. Required knowledge covered by Topic 1.1 (5 marks)
We consider a directed, unweighted graph stored by the adjacency list
(an array of out-neighbors is stored for each vertex). Design an
algorithm to compute the shortest distance between two query
vertices (i.e., the input is two vertex IDs, and the output should be the
shortest distance). The queue data structure is not allowed in your
solution (e.g., the dequeue object in Python). Please write your
pseudocode and justify the time complexity of each subpart, as well as
the total time complexity of your algorithm.
2024/6/5 15:03 COMP9312 24T2 Assignment 1
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Marking for Q6: Two factors are evaluated in marking: (1) How good is
your time complexity; (2) Does your algorithm match your time
complexity. Full marks are given if your time complexity is not larger
than our expected one and your algorithm corresponds with your time
complexity.
END OF QUESTIONS
2024/6/5 15:03 COMP9312 24T2 Assignment 1
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