IE 598 Inference in Graphical Models
Homework 3
Due-11/06/2012
Please return this homework in class, to Transportation 117 by 4:30 pm, or by email to [email protected]
Problem 3.1
Consider the following graphical model.
(a) Draw a factor graph representi
IE 512 Graphs, Networks, and Algorithms
Homework 5 Solution
Solution 7.1
(a) Let xi cfw_0, 1 be whether an actor i is in the cast or not, and yj be whether an investor j is funding
n
m
the movie or not. Then, the total prot is k=1 si xi + j =1 pj yj . And
IE 512 Graphs, Networks, and Algorithms
Homework 7 Solution
Problem 7.2
Cost of buying is B and renting is R. Consider a strategy of renting till time t 1
and buying if t-th ski trip happened. The worst case data for this strategy is if there are exactly
IE 512 Graphs, Networks, and Algorithms
Homework 2 Solution
Problem 2.1
We use a similar algorithm as the stable marriage problem, but modied slightly for
this particular problem.
WHILE there exists colleges engaged to strictly less than ci students
Each
IE 512 Graphs, Networks, and Algorithms
Homework 1 Solution
Problem 1.1 Consider a graph G = (V, E), where V is the set of vertices each corresponding to an
agent, and we connect to agents with an edge if those two agents know the identity of each other.
IE 512 Graphs, Networks, and Algorithms
Homework 6 Solution
Solution 6.1
(a) Let xi cfw_0, 1 be whether an actor i is in the cast or not, and yj be whether an investor j is funding
n
m
the movie or not. Then, the total prot is k=1 si xi + j=1 pj yj . And
IE 512 Graphs, Networks, and Algorithms
Homework 1 Solution
Problem 1.1 Consider a graph G = (V, E ), where V is the set of vertices each corresponding to an
agent, and we connect to agents with an edge if those two agents know the identity of each other.
IE 512 Graphs, Networks, and Algorithms
Homework 2 Solution
Problem 2.1 We want to show that at least one of G = (V, E ) and G = (V, E ) is connected. Here, G
if and only if they
is a graph on the vertices of G such that two vertices are adjacent (i.e. c
IE 512 Graphs, Networks, and Algorithms
Homework 4 Solution
Problem 4.1
We use a similar algorithm as the stable marriage problem, but modied slightly for
this particular problem.
WHILE there exists colleges engaged to strictly less than ci students
Each
IE 512 Graphs, Networks, and Algorithms
Homework 5 Solution
Problem 5.1
Consider a network N = (V, E), where the source is connected to all the male students, all female
students are connected to the sink, and we add directed edges from a male student to