CS252 Algorithms
Wednesday, 9 November 2022

+ Later today
- Scores up to date, grade status update sent out
- If you want your exam before Friday, you can come
    get it during my Thursday office hours (or if you
    can catch me some other time Thursday--which might
    be difficult)

+ Friday
- Wrap-up on network flows
    - look at the flight scheduling problem in 7.9
- Beginning of "fun miscellaneous algorithms week"
    (start with the Art Gallery Problem as an
     entry into Computational Geometry)

+ Monday
- Exam posted
- More fun miscellaneous algorithms

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+ Network flows, continued
- Definitions: flow network, source, sink, capacity
               flow, residual graph, augmenting path
- Max flow algorithm (Ford-Fulkerson)

- Questions: does it terminate?; does it maximize
    the flow? how long does it take?

- Definitions: cut, min cut
- Theorem: max-flow, min-cut

+ Let's try some applications
- Bipartite matching as a very simple example
- Rooms & classes during 3A
    - Maximize number of classes with a room
    - Maximize the number of students with a room

+ Problem set #6
- Write up the rooms & classes problem
- K&T 

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+ Algorithm (Ford-Fulkerson)
Initialize f to be f(e) = 0 for all e in E
Initialize residual graph G_f accordingly
while there exists a path P from s to t in the G_f:
    let "bottleneck" of P be the minimum edge capacity in P
    push bottleneck's worth of flow onto all edges in P
        and update f and G_f accordingly