hw_08 - CS 473 Fundamental Algorithms Spring 2012 Homework...

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CS 473: Fundamental Algorithms, Spring 2012 Homework 8 (due Tuesday, 23:55:00, April 3, 2012) See homework 1. Each student individually have to also do quiz 8 online. Version: 1.3 1. ( 35 pts. ) Recomputing correct ﬂow. Given a ﬂow network G with integer capacities you have computed a maximum ﬂow f between s and t . However you have made a mistake in noting the capacity of an edge e . (15 pts) Suppose you under estimated the capacity of e by k > 0 units. Show that you can compute the correct maximum ﬂow in O ( km ) time using the current ﬂow f . (20 pts) Do the same as above if you over estimated the capacity of e by k > 0 units. Hint: First assume that f is acyclic. How do you reduce ﬂow on e ? 2. ( 35 pts. ) Special minimum cuts. Let G = ( V,E ) be a ﬂow network with integer edge capacities. We have seen algorithms that compute a minimum s - t cut. For both problems below assume that you only have black box access to an algorithm that given

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This note was uploaded on 04/02/2012 for the course CS 473 taught by Professor Chekuri,c during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw_08 - CS 473 Fundamental Algorithms Spring 2012 Homework...

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