a G 6 ` a a z 6 bw4yrdd@qhI iq rcfw_9 G6 ` b4yrdd@qh a a a irI Yq ` pE ` Bxqh ` n Hf V 3 m6 G E H Va 3p 1 E8 p ~68 6 8 1E m s ~ pE k p 1 E s kE g XrBiBrcfw_$BXlwx4m@6x534riUe4GenXqweBBl4Xe HR2UiRi74UiRUiUABE S4Xbx4x7bB4E)e@R4G@XGBcfw_sf G6 h 3Q G3 1 3
Inverting Matrix
AX = I X = A-1 How hard is the matrix inversion problem?
Matrix inversion
Theorem: Multiplication is as hard as inversion
Proof: Let I(n) be the cost of inversion. Let M(n) be the cost of multiplication. Want to show I(n) = (M(n).
M(n)=O(
Network with multiple sources and sinks
15
Maximum bipartite matching
t1
a
b
19
s1
Bipartite graph G=(V,E):
Undirected V = V1V2, V1V2=. e=(u, v)E, uV1 and vV2
s
s2
14
c e
9
d b k
4
30
11
9
t2
13 12
t
s3
1 5
f g
d b
t3
4
h
d
23
Complete bipartite: u V1, u
Contents
Maximum flow problem. Minimum cut problem. Max-flow min-cut theorem. Augmenting path algorithm. Capacity-scaling. Shortest augmenting path.
Max-Flow Min-Cut Theorem
MAX-FLOW MIN-CUT THEOREM (Ford-Fulkerson, 1956): In any network, the value of the
Chapter 26
Contents
Contents.
Maximum flow problem. Minimum cut problem. Max-flow min-cut theorem. Augmenting path algorithm. Capacity-scaling. Shortest augmenting path.
Maximum Flow
How do we transport the maximum amount data from source to sink?
Some of
Chapter 26
Contents
Contents.
Maximum flow problem. Minimum cut problem. Max-flow min-cut theorem. Augmenting path algorithm. Capacity-scaling. Shortest augmenting path.
Maximum Flow
How do we transport the maximum amount data from source to sink?
Some of
Road map
Objective
Modules
Breadth first search (Bfs)
Ford-Fulkerson
Image Partitioning
Test case
Theoretical Analysis and Experimental
Results
Objective
The objective of this project is to segment
an image using Ford-Fulkerson Algorithm.
To implement a s