16-max-flow-handout.pdf

# 16-max-flow-handout.pdf - Algorithm Design Techniques...

• Notes
• 5

This preview shows 1 out of 3 pages.

CMPSCI 311: Introduction to Algorithms Lecture 16: Network Flows Akshay Krishnamurthy University of Massachusetts Last Compiled: April 3, 2018 Algorithm Design Techniques Greedy Divide and Conquer Dynamic Programming Network Flows Network Flow Previous topics (greedy, dynamic programming, divide and conquer etc.) were design techniques. Network flow relates to a specific class of problems with many applications Direct applications : commodities in networks transporting food on the rail network packets on the internet gas through pipes Indirect applications : Matching in graphs Airline scheduling Baseball elimination Plan : design and analyze algorithms for max-flow problem , then apply to solve other problems First, a Story About Flow and Cuts Key theme : flows in a network are intimately related to cuts Soviet rail network in 1955 On the history of the transportation and maximum flow problems. Alexander Schrijver, Math Programming, 2002. Capacity v 1 v 2 v 3 v 4 t s 16 13 14 9 12 4 7 20 4 Capacity/Flow v 1 v 2 v 3 v 4 t s 16/11 13/8 14/11 9/4 12/12 4/1 7/7 20/15 4/4

Subscribe to view the full document.

Defining Flows Flow network Directed graph Source node s and target node t Edge capacities c ( e ) 0 Flow Capacity Constraints: 0 f ( e ) c ( e ) on each edge Conservation Constraints: f in ( s ) = 0 , f out ( t ) = 0 , v V \{ s, t } f in ( v ) = f out ( v ) where f in ( v ) = e in to v f ( e ) and f out ( v ) = e out of v f ( e ) Max flow problem: find a flow of maximum value v ( f ) = f out ( s ) Designing a Max-Flow Algorithm Something that doesn’t work: Repeatedly choose paths and
You've reached the end of this preview.
• Fall '09
• Flow network, Maximum flow problem, Max-flow min-cut theorem, New Flow, Old Flow, Flow f

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern