Data Matters

1
233-234
Sedgewick Wayne (2004) Chazelle (2005)
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
How to check if adding an edge creates a cycle?
Label i all nodes of i-th tree
1
2
1
2
1
2
2
11
How to check if adding an edge creates a cycle?
Label i all nodes of i-th tree
1
2
1
2
1
2
2
12
How to check if adding an edge creates a cycle?
Label i all nodes of i-th tree
1
2
1
2
1
2
2
Relabel smaller tree
13
How to check if adding an edge creates a cycle?
Label i all nodes of i-th tree
2
2
2
2
2
2
2
Relabel smaller tree
14
How to check if adding an edge creates a cycle?
Label i all nodes of i-th tree
2
2
2
2
2
2
2
Each node relabeled at most log V times
15
(No Transcript)
16
edge of the MST
correctness
9
3
B nodes
7
8
A nodes
17
B
3
A
18
B
3
A
A
B
A
A
8
19
How much time ?
1. Sorting
2. Cycle detection
20
How much time ?
1. Sorting
2. Cycle detection
Time proportional to
21
Advanced MST Algorithms
Yao/Cheriton-Tarjan (1976)
Fredman-Tarjan (1984)
Gabow-Galil-Spencer-Tarjan (1986)
Chazelle (2000)
22
Ackermanns function
number of particles in the universe
If E 2
23

• The amazing function

Tower of height equal to tower of x
Two times x
Tower of x
Two to the x-th
24

• demo time