02-713: Homework #1
Due: Jan. 24 by the start of class
You may discuss these problems with your current classmates, but you must write up your
solutions independently, without using common notes or worksheets. You must indicate at the
top of your homework
Shortest Paths in a Graph
Slides by Carl Kingsford
Feb. 5, 2014
Based on/Reading: Chapter 4.5 of Kleinberg & Tardos
Shortest Paths in a Weighted, Directed Graph
Given a directed graph G with lengths
e
> 0 on each edge e:
u
1
1
x
4
s
2
1
2
1
3
v
w
z
3
y
Go
02-713 Introduction
Slides by Carl Kingsford
Jan. 13, 2014
KT Chapter 1
Objective of this Course
To study general computational problems and their algorithms,
with a focus on the principles used to design those algorithms.
After passing this class, you sh
02-713 Homework #3: Graph Traversals
Due: Feb. 13 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your
homework wh
02-713 Homework #4: Shortest Paths
Due: Feb. 22 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your
homework who
02-713 Homework #1:
Due: Jan. 28 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your
homework who you worked with
02-713 Homework #6: Divide and Conquer
Due: Mar. 29 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indicate at the top of your homework
02-713 Homework #5: Traveling Salesman and A*
Due: Mar. 18 by 9:30am
Introduction. Let V = cfw_u1 , . . . , un be a set of cities and let d(ui , uj ) = d(uj , di ) be the (symmetric) distance between city ui and uj . The optimal traveling salesman tour o
02-713 Homework #7: Dynamic Programming
Due: Apr. 10 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indicate at the top of your homework
02-713 Homework #2: Asymptotic Analysis
Due: Feb. 4 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your
homework
02-713 Homework #8: Network Flow
Due: Apr. 24 by 9:30am
You may discuss these problems with your classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indicate at the top of your homework
who yo
Clustering with Minimum Spanning Tree
Slides by Carl Kingsford
Jan. 24, 2014
KT 4.6
Clustering: an application of
MST
Clustering
Youre given n items and the distance d(u, v ) between each of
pair.
d(u, v ) may be an actual distance, or some abstract repre
Shortest Paths with Negative Weights
Slides by Carl Kingsford
Feb. 12, 2013
Based in part on Section 6.8
1
Shortest Path Problem
Shortest Path with Negative Weights. Given directed graph G with
weighted edges d(u, v ) that may be positive or negative, nd
02-713 Homework #3: Graph Traversals
Due: Feb. 7 by 9:30am
You may discuss these problems with your current classmates, but you must write up your
solutions independently, without using common notes or worksheets. You must indicate at the top
of your home
02-713 Homework #4: Shortest Paths
Due: Feb. 12 by 11:59pm Note unusual time
You may discuss these problems with your current classmates, but you must write up your
solutions independently, without using common notes or worksheets. You must indicate at th
02-713 Homework #5
Due: Mar. 3 by 9:30am
You may discuss these problems with your current classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indicate at the top of your homework
who you worke
02-713 Homework #6: Dynamic Programming
Due: Mar. 7 by 11:59pm (note the unusual time)
You may discuss these problems with your current classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indi
02-713 Homework #2
Due: Jan. 31 by 9:30am
You may discuss these problems with your current classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your homework
who you work
02-713 Homework #8: Sux Trees
Due: Apr. 9 by 9:30am
You may discuss these problems with your current classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of your
homework wh
02-713 Homework #7: Dynamic Programming II
Due: Mar. 24 by 9:30am
You may discuss these problems with your current classmates, but you must write up your solutions
independently, without using common notes or worksheets. You must indicate at the top of yo
02-713 Homework #9: Network Flow
Due: Apr. 16 by 9:30am
Dont use last years solutions. Dont look up solutions in the web. The point of these homeworks is to
prepare for the exams.
You may talk with your classmates about these problems, but you must write
02-713 Homework #10: Linear Programming
Due: Apr. 28 by 9:30am
Dont look up solutions in the web. The point of these homeworks is to prepare for the exams. You may
talk with your classmates about these problems, but you must write up your solutions indepe
Approximation Algorithms, I:
Traveling Salesman
Slides by Carl Kingsford
Jan. 20, 2014
Approximation Algorithms
How do we deal with problems where we dont have an
ecient algorithm?
One option: heuristics
But wed like some guarantee: the answer we get shou
02-713 Homework #9: NP-completeness
Due: May 1 by 5pm
You may discuss these problems with your classmates, but you must write up your solutions independently, without using common notes or worksheets. You must indicate at the top of your homework
who you