CS 473g: Algorithms, Fall 2007
Midterm October 4, 2007
Name:
Net ID:
Alias:
This is a closed-book, closed-notes, open-brain exam. If you brought anything with you besides
writing instruments and your handwritten 8 1 11 cheat sheet, please leave it at the
CS 473: Algorithms
Chandra Chekuri chekuri@cs.illinois.edu 3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Depth First Search Directed Graphs
Searching
Strong Connected Components (SCCs) cted Graphs
B A C
E
F
D
G
H
De
CS 473
Head-Banging 1 (January 27 and 28, 2009)
Spring 2009
1. An inversion in an array A[1 . n] is a pair of indices (i , j ) such that i < j and A[i ] > A[ j ]. The
n
number of inversions in an n-element array is between 0 (if the array is sorted) and 2
CS 573: Graduate Algorithms, Fall 2011
HW 4 (due in class on Tuesday, November 1st)
This homework contains ve problems. Read the instructions for submitting homework on
the course web page. In particular, make sure that you write the solutions for the pro
CS 473
HBS 7
Spring 2009
CS 473: Undergraduate Algorithms, Spring 2009
HBS 7
1. Let G = (V, E ) be a directed graph with non-negative capacities. Give an efcient algorithm to
check whether there is a unique max-ow on G?
2. Let G = (V, E ) be a graph and s
CS 473
HBS 6.55
Spring 2009
CS 473: Undergraduate Algorithms, Spring 2009
HBS 6.55
1. Suppose you are given a directed graph G = (V, E ) with non-negative edge lengths; (e) is the
length of e E . You are interested in the shortest path distance between tw
CS 573: Graduate Algorithms, Fall 2011
HW 1 (due Tuesday, September 13th)
This homework contains ve problems. Read the instructions for submitting homework on
the course webpage. In particular, make sure that you write the solutions for the problems on
se
CS 573: Algorithms, Fall 2009
Homework 3, due Wednesday, October 28, 23:59:59, 2009 Version 1.0
Name: Net ID:
# 1. 2. 3. 4. Total
Alias:
Score Grader
Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Staple
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Complementation
Self Reduction
Part I
Complementation and Self-Reduction
Chekuri
CS473ug
Complementation
Self
CS 573
Homework 5 (due November 19, 2010)
Fall 2010
CS 573: Graduate Algorithms, Fall 2010
Homework 5
Due Friday, November 19, 2010 at 5pm
(in the homework drop boxes in the basement of Siebel)
1. Suppose we are given a set of boxes, each specied by their
CS CS 473g: Algorithms, Fall 2007
Homework 3 (due Tuesday, October 23, 2007 at 11:59.99 p.m.)
Version 1.02
Required Problems
1. The good, the bad, and the middle.
[20 Points]
Suppose youre looking at a ow network G with source s and sink t, and you want t
CS 573: Algorithms, Fall 2013
Homework 3: Solutions
Version 1.0
1. Prove infeasibility. (25 pts.)
You are trying to solve a circulation problem, but it is not feasible. The problem has demands, but no
capacity limits on the edges. More formally, there is
CS 473U: Undergraduate Algorithms, Fall 2006
Homework 0
Due Friday, September 1, 2006 at noon in 3229 Siebel Center
Name:
Net ID:
Alias:
I understand the Homework Instructions and FAQ.
Neatly print your full name, your NetID, and an alias of your choice
CS 573: Graduate Algorithms, Fall 2008
Homework 0
Due in class at 12:30pm, Wednesday, September 3, 2008
Name:
Net ID:
Alias:
I understand the course policies.
Each student must submit their own solutions for this homework. For all future homeworks,
group
CS 473
Midterm 1 Questions Version 1
Spring 2010
This exam lasts 120 minutes.
Write your answers in the separate answer booklet.
Please return this question sheet with your answers.
1. Each of these ten questions has one of the following ve answers:
A: (1
CS 573
Midterm 1 Questions
Fall 2010
This exam lasts 90 minutes.
Write your answers in the separate answer booklet.
Please return this question sheet with your answers.
1. (a) Suppose A[1 . n] is an array of n distinct integers, sorted so that A[1] < A[2]
CS 473
Midterm 2 Questions Version
Spring 2010
This exam lasts 120 minutes.
Write your answers in the separate answer booklet.
Please return this question sheet with your answers.
1. Find the following spanning trees for the weighted graph shown below.
s
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Ford-Fulkerson Algorithm
Correctness and Analysis
Polynomial Time Algorithms
Part I
Algorithm(s) for Maximum F
CS 473
Midterm 2 Questions (April 7, 2009)
Spring 2009
You have 90 minutes to answer four of the five questions.
Write your answers in the separate answer booklet.
You may take the question sheet with you when you leave.
1. Recall that a tree is a connect
CS 573
Midterm 2 Questions
Fall 2010
This exam lasts 90 minutes.
Write your answers in the separate answer booklet.
Please return this question sheet with your answers.
1. Assume we have access to a function RANDOM(k) that returns, given any positive inte
CS 373: Combinatorial Algorithms, Fall 2000
Midterm 1 October 3, 2000
Name: Net ID:
Alias:
This is a closed-book, closed-notes exam!
U 3/4 1
If you brought anything with you besides writing instruments and your 8 1 11 cheat sheet, please leave it at the f
CS 373
Midterm 1 Questions (February 20, 2001)
Spring 2001
Write your answers in the separate answer booklet.
1. Multiple Choice: Each question below has one of the following answers. (a) (1) (b) (log n) (c) (n) (d) (n log n) (e) (n2 )
For each question,
CS 573: Algorithms, Fall 2009
Midterm October 7, 2009, 79 PM
Transportation building, 103
Name:
Net ID:
Alias:
This is a closed-book, closed-notes, open-brain exam. If you brought anything with you
1
besides writing instruments and your handwritten 8 2 1
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473
Part I
Heuristics
Chekuri
CS473
Coping with Intractability
Some general things that people do.
Consider special
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
The Satisability Problem (SAT)
Sat and 3-SAT
3-SAT and Independent Set
Part I
Reductions Continued
Chekuri
CS4
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Overview
Denitions
Part I
Introduction to Reductions
Chekuri
CS473ug
Overview
Denitions
Reductions
A reduction
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Introduction
Solving Linear Programs
Duality
Integer Linear Programming
Part I
Introduction to Linear Programm
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Recap
NP: languages that have polynomial time certiers/veriers
Chekuri
CS473ug
Recap
NP: languages that have p
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Knapsack
Part I
Knapsack
Chekuri
CS473ug
Knapsack
Knapsack Problem
Input Given a Knapsack of capacity W lbs. a
CS 473: Algorithms
Chandra Chekuri
chekuri@cs.illinois.edu
3228 Siebel Center
University of Illinois, Urbana-Champaign
Fall 2009
Chekuri
CS473ug
Part I
Baseball Pennant Race
Chekuri
CS473ug
Pennant Race
Chekuri
CS473ug
Pennant Race: Example
Example
Team
N