Question 1 Which of the following graph representations would be the most performant for a graph where: • Each vertex has at most three edges incident on it The predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations are used equally often Assume that the computers being used do not have memory constraints. (a) O Adjacency Matrix Adiacency List

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Question 1
Which of the following graph representations would be the most performant for a graph where:
• Each vertex has at most three edges incident on it
The predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations are
used equally often
Assume that the computers being used do not have memory constraints.
(a) O
Adjacency Matrix
(b) O
Adjacency List
(c) O
Array of Edges
Question 2
Consider the components algorithm from the lectures that assigns vertices to connected components. What is the worst case time
complexity of the algorithm, assuming that the graph uses the adjacency matrix representation?
Note: In the time complexities below, V and E refer to the number of vertices and edges in the graph respectively.
(a) O
(b) O
O(V^2)
(c) O
O(V^3)
(d) O
O(V + E)
(e) O
OVV + E))
Transcribed Image Text:Question 1 Which of the following graph representations would be the most performant for a graph where: • Each vertex has at most three edges incident on it The predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations are used equally often Assume that the computers being used do not have memory constraints. (a) O Adjacency Matrix (b) O Adjacency List (c) O Array of Edges Question 2 Consider the components algorithm from the lectures that assigns vertices to connected components. What is the worst case time complexity of the algorithm, assuming that the graph uses the adjacency matrix representation? Note: In the time complexities below, V and E refer to the number of vertices and edges in the graph respectively. (a) O (b) O O(V^2) (c) O O(V^3) (d) O O(V + E) (e) O OVV + E))
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