The Minimum Cost Spanning Tree Problem - PowerPoint PPT Presentation

Loading...

PPT – The Minimum Cost Spanning Tree Problem PowerPoint presentation | free to view - id: 142f4a-MjZjN



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

The Minimum Cost Spanning Tree Problem

Description:

The relationship between shortest path and matrix multiplication. Faster-All-Pairs-Shortest-Paths algorithm. Floyd-Warshall algorithm. Puzzle 1. Puzzle 2 ... – PowerPoint PPT presentation

Number of Views:131
Avg rating:3.0/5.0
Slides: 69
Provided by: ding8
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: The Minimum Cost Spanning Tree Problem


1
Lecture 11
  • The Minimum Cost Spanning Tree Problem

2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
a
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
Correctness
20
The Greedy Algorithm
  • animation

21
The Greedy Algorithm in Action
4
2
6
1
5
3
7
22
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
23
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
24
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
25
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
26
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
27
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
28
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
29
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
30
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
31
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
32
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
33
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
34
(No Transcript)
35
(No Transcript)
36
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 2 3 4 5
4 7
10
8
10
8
2
4
6
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
36
37
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 3 4 5
4 7
10
8
10
8
2
4
6
2
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
37
38
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 3 4 5
4 5
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
7
5
3
7
15
15
11
38
39
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 5 4 5
4 5
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
7
3
5
3
7
15
15
11
39
40
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 4 4 4
4 4
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
7
3
5
3
7
15
15
11
40
41
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 4 4 4 4 4
4 4
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
3
5
3
7
15
15
11
41
42
(No Transcript)
43
(No Transcript)
44
Correctness
  • The cut-optimality Condition

45
Prims algorithm
  • animation

46
Prims Algorithm in Action
10
8
4
4
6
2
2
6
35
15
1
1
25
20
30
17
21
11
40
5
7
3
5
3
7
15
The minimum cost arc from yellow nodes to green
nodes can be found by placing arc values in a
priority queue.
47
Prims Algorithm in Action
8
10
4
4
6
2
2
2
6
35
35
15
1
25
1
30
20
17
21
11
40
5
7
3
5
3
7
15
48
Prims Algorithm in Action
8
10
10
10
4
2
2
4
6
4
2
6
35
35
15
1
25
25
1
30
17
20
21
11
40
5
7
3
5
3
7
15
49
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
1
25
25
1
17
30
30
20
20
21
21
11
40
5
7
3
5
3
7
15
50
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
40
5
7
3
5
5
3
7
15
51
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
40
5
7
3
5
5
3
7
15
52
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
3
7
5
7
5
3
7
15
15
53
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
54
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
55
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
56
(No Transcript)
57
(No Transcript)
58
Correctness
  • Cut-optimality Condition

59
Sollins Algorithm
  • animation

60
Sollins Algorithm in Action
10
8
4
4
6
2
4
6
2
2
6
35
15
1
1
1
25
20
30
17
21
40
5
7
3
5
7
3
5
3
7
11
15
Treat all nodes as singleton components, and then
select the min cost arc leaving the component.
61
Sollins Algorithm in Action
10
8
4
4
6
2
6
2
6
35
15
1
1
25
20
30
17
21
40
5
7
3
7
3
5
5
3
7
11
15
Find the min cost edge out of each component
62
(No Transcript)
63
Appendix Priority Queue
64
Priority Queue
  • A priority queue is a data structure for
    maintaining a set of elements, each with an
    associated value, called a key.
  • A min-priority queue supports the following
    operations Insert(S,x), Minimum(S),
  • Extract-Min(S), Increase-Key(S,x,k).
  • Min-Heap can be used for implementing
  • min-priority queue.

65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
About PowerShow.com