21.2-4 Suppose that all edge weights in a graph are integers in the range from 1 to [V]. How fast can you make Kruskal's algorithm run? What if the edge weights are integers in the range from 1 to W for some constant W? Kruskal's algorithm Kruskal's algorithm finds a safe edge to add to the growing forest by finding, of all the edges that connect any two trees in the forest, an edge (u, v) with the lowest weight. Let C₁ and C₂ denote the two trees that are connected by (u, v). Since (u, v) must be a light edge connecting C₁ to some other tree, Corollary 21.2 implies that (u, v) is a safe edge for C₁. Kruskal's algorithm qualifies as a greedy algorithm because at each step it adds to the forest an edge with the lowest possible weight. 9 (1) 11 14 11 14 7 8 10 10 (K) a 11 14 (1) 11 7. 7. 6 10 (0 4 (m) a 11 7. 6 8 Figure 21.4, continued Further steps in the execution of Kruskal's algorithm. b 14 11 1 141 7 6 10 10 2 1
21.2-4 Suppose that all edge weights in a graph are integers in the range from 1 to [V]. How fast can you make Kruskal's algorithm run? What if the edge weights are integers in the range from 1 to W for some constant W? Kruskal's algorithm Kruskal's algorithm finds a safe edge to add to the growing forest by finding, of all the edges that connect any two trees in the forest, an edge (u, v) with the lowest weight. Let C₁ and C₂ denote the two trees that are connected by (u, v). Since (u, v) must be a light edge connecting C₁ to some other tree, Corollary 21.2 implies that (u, v) is a safe edge for C₁. Kruskal's algorithm qualifies as a greedy algorithm because at each step it adds to the forest an edge with the lowest possible weight. 9 (1) 11 14 11 14 7 8 10 10 (K) a 11 14 (1) 11 7. 7. 6 10 (0 4 (m) a 11 7. 6 8 Figure 21.4, continued Further steps in the execution of Kruskal's algorithm. b 14 11 1 141 7 6 10 10 2 1
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
Problem 1PE
Related questions
Question
![21.2-4
Suppose that all edge weights in a graph are integers in the range from 1 to [V]. How fast can
you make Kruskal's algorithm run? What if the edge weights are integers in the range from 1 to
W for some constant W?
Kruskal's algorithm
Kruskal's algorithm finds a safe edge to add to the growing forest by finding, of all the edges that connect any two trees in the forest, an edge (u, v) with the lowest weight. Let
C₁ and C₂ denote the two trees that are connected by (u, v). Since (u, v) must be a light edge connecting C₁ to some other tree, Corollary 21.2 implies that (u, v) is a safe edge
for C₁. Kruskal's algorithm qualifies as a greedy algorithm because at each step it adds to the forest an edge with the lowest possible weight.
9
(1)
11
14
11
14
7
8
10
10
(K)
a
11
14
(1)
11
7.
7.
6
10
(0
4
(m) a
11
7.
6
8
Figure 21.4, continued Further steps in the execution of Kruskal's algorithm.
b
14
11
1
141
7
6
10
10
2
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3fa098a-800d-440b-b28a-d62ad7aee48d%2F01a24f34-1a29-49cd-9a12-c47c97a5a5c7%2Fn107bqj9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:21.2-4
Suppose that all edge weights in a graph are integers in the range from 1 to [V]. How fast can
you make Kruskal's algorithm run? What if the edge weights are integers in the range from 1 to
W for some constant W?
Kruskal's algorithm
Kruskal's algorithm finds a safe edge to add to the growing forest by finding, of all the edges that connect any two trees in the forest, an edge (u, v) with the lowest weight. Let
C₁ and C₂ denote the two trees that are connected by (u, v). Since (u, v) must be a light edge connecting C₁ to some other tree, Corollary 21.2 implies that (u, v) is a safe edge
for C₁. Kruskal's algorithm qualifies as a greedy algorithm because at each step it adds to the forest an edge with the lowest possible weight.
9
(1)
11
14
11
14
7
8
10
10
(K)
a
11
14
(1)
11
7.
7.
6
10
(0
4
(m) a
11
7.
6
8
Figure 21.4, continued Further steps in the execution of Kruskal's algorithm.
b
14
11
1
141
7
6
10
10
2
1
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