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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 Spring '08
 Chekuri,C
 Algorithms, Combinatorial optimization, valid committee assignment

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