Math566 - HW 1 Due on Thursday, Sep 4
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 1
1. For the shortest path problem, add arc (t, s) with lts = uts = 1, and cts = 0. For the original network, set
lij = 0, uij 1. The condition uts = 1 ca
Math566 - HW 9 Due on Thursday, Oct 30
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 9
1. We rst try to nd a feasible ow in the given network. For this purpose, we can create an
equivalent network with
uij = uij lij (i, j) A, and b(i) =
l
Math566 - HW 12 Due on Thursday, Dec 11
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 12
1. An MST need not be a tree of shortest paths. See the network, MST, and shortest path tree
shown here.
2
2
2
1
1
1
4
1
1
3
2.
2
1
2
4
1
1
3
1
4
1
1
Math 466/566 - Midterm
1
Network Optimization (Fall 2014) Midterm Exam
Name:
There are eight problems on four pages.
The total points (given in parentheses) add up to 105. You will be graded for 100 points.
1. (10) Identify all directed cycles in the foll
Math566 - HW 6 Due on Thursday, Oct 16
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 7
1. There is a small typo in the Bellman equations. It should read
d(j) = mincfw_ d(i) + cij : (i, j) AI(j) for all j N.
(a) The shortest path distances
Math 466/566 - HW 4 Due on Friday, Sep 26
1
Network Optimization (Fall 2014) Homework 4
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You must attempt problem 6 for your homework submission to be valid
Math566 - HW 2 Due on Thursday, Sep 11
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 2
1.
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2. Follows directly from the denition of a strongly connected (directed) graph.
Math566 - HW 4 Due on Friday, Sep 26
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 4
1. First-t heuristic
LIST := cfw_a1 , . . . , an ;
num Bins := 0; (number of bins)
Cap := ; (vector of available bin capacities, size is variable)
Bin Id
Math566 - HW 8 Due on Thursday, Oct 23
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 8
1. When cpq is decreased to cpq , any i-j shortest path that originally used (p, q) will continue
to use it. Further, some i-j shortest paths that did
Math566 - HW 6 Due on Tuesday, Oct 7
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 6
1.
(a) False. The shortest path length will not be affected if you remove an arc which is not
on the shortest path. See rst network in Figure 1 removing
Math 466/566 - HW 10 Due on Thursday, Nov 6
1
Network Optimization (Fall 2014) Homework 10
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You must attempt problem 6 for your homework submission to be va
Math566 - HW 11 Due on Thursday, Nov 20
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 11
1.
(a) The cycles in G(x ) are W1 = 1-4-3-2-1, W2 = 3-5-7-4-3, W3 = 1-4-3-5-6-2-1,
and W4 = 1-4-3-5-7-8-6-2-1. As demonstrated on the residual networ
Math566 - HW 5 Due on Thursday, Oct 2
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 5
1. The set of paths ands cycles can be P = cfw_P1 , P2 , P3 = cfw_1-2, 1-2-4-5, 1-3-2-4-5, W =
cfw_W1 , W2 = cfw_2-4-5-2, 2-4-5-3-2 with f (P1 ) = 5,
Math566 - HW 10 Due on Thursday, Nov 6
1
Network Optimization (Fall 2014)
Brief Solutions to Homework 10
1.
(a) FALSE. In the counterexample, numbers given are uij s.
=
2
3
1
!
/
2
1
3
(b) FALSE. Values shown are xij , uij pairs. Deleting (1, 3) with maxi
Math 466/566 - HW 5 Due on Thursday, Oct 2
1
Network Optimization (Fall 2014) Homework 5
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You must attempt problem 6 for your homework submission to be vali
Math 466/566 - HW 8 Due on Thursday, Oct 23
1
Network Optimization (Fall 2014) Homework 8
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
Exercises marked with a [G] target the graduate students (Math 56
Math 466/566 - HW 3 Due on Thursday, Sep 18
1
Network Optimization (Fall 2014) Homework 3
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
Exercises marked with a [G] target the graduate students (Math 56
Math 466/566 - HW 11 Due on Thursday, Nov 20
1
Network Optimization (Fall 2014) Homework 11
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
Exercises marked with a [G] target the graduate students (Math
Math 466/566 - HW 9 Due on Thursday, Oct 30
1
Network Optimization (Fall 2014) Homework 9
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You must attempt problem 6 for your homework submission to be val
Math 466/566 - HW 7 Due on Thursday, Oct 16
1
Network Optimization (Fall 2014) Homework 7
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You must attempt problem 5 for your homework submission to be val
Math 466/566 - HW 6 Due on Tuesday, Oct 7
1
Network Optimization (Fall 2014) Homework 6
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
The total points (given in parentheses) add up to 65. Both Math 466
Math 466/566 - HW 1 Due on Thursday, Sep 4
1
Network Optimization (Fall 2014) Homework 1
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
Exercises marked with a [G] target the graduate students (Math 566
Math 466/566 - HW 2 Due on Thursday, Sep 11
1
Network Optimization (Fall 2014) Homework 2
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
Exercises marked with a [G] target the graduate students (Math 56
Math 466/566 - Practice Midterm
1
Network Optimization (Fall 2014) Practice Midterm
The total points (given in parentheses) add up to 105. You will be graded for 100 points.
Try to give brief answers.
Time is precious. anonymous.
1. (10) Give the BFS and
Math 466/566 - HW 12 Due on Thursday, Dec 11
1
Network Optimization (Fall 2014) Homework 12
AMO stands for the text (Ahuja, Magnanti, Orlin). Exercises and page numbers are listed
from AMO.
You will be graded for 80 points.
You must email your submissi