Download presentation

Presentation is loading. Please wait.

Published byJosh Kinder Modified over 4 years ago

1
Maximum flow problems IV. MA252 Combinatorial Optimization

2
t t s s Auxiliary graph t t s s

3
Exponentially many steps t t s s

4
t t s s

5
Application Transportation problem Factories Retail stores Requirement for goods Production capacity... Can factories satisfy the demand of retail stores ? aiai aiai bjbj bjbj edge if i-th factory can deliver to j-th store t Maximum flow capacity limited production (capacity) limited demand (capacity) source target a1a1 a2a2 anan bmbm b1b1 b2b2 s

6
Application Transportation problem Factories Retail stores Requirement for goods Production capacity... Can factories satisfy the demand of retail stores ? t Maximum flow capacity limited production (capacity) limited demand (capacity) Units of flow 1 23 source target bmbm b1b1 b2b2 Example 1: n=m=3 a 1 =a 2 =a 3 =1 b 1 =b 2 =b 3 =1 Answer: Yes! a1a1 a2a2 anan s

7
Application Transportation problem Factories Retail stores Requirement for goods Production capacity Can factories satisfy the demand of retail stores ? t Maximum flow capacity limited production (capacity) limited demand (capacity) source target Example 2: n=m=3 a 1 =a 2 =1 a 3 =3 b 1 =3 b 2 =b 3 =1 Answer: No! Maximum flow = 4 < 5 3 rd factory does not deliver to 1 st retail store s Example 1: n=m=3 a 1 =a 2 =a 3 =1 b 1 =b 2 =b 3 =1

8
Summary of Flow Problems problem nameparametersquestion Connectivity Shortest path Maximum flow Minimum cost flow

Similar presentations

OK

IEOR 4004 Maximum flow problems. Connectivity t t s s Q1: Can Alice send a message to Bob ? Yes if every (s,t)-cut contains at least one forward edge.

IEOR 4004 Maximum flow problems. Connectivity t t s s Q1: Can Alice send a message to Bob ? Yes if every (s,t)-cut contains at least one forward edge.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google