Fall 2001 CS170
Fall 2001
CS170: Efficient Algorithms and Intractable Problems
Professor Luca Trevisan
Midterm 2
Problem 1.
Provide the following information
Your name:
Your SID number:
Your section number (and/or your TA name):
Name of the person on your

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CS170 Review Session
7:00-9:00, Hearst Annex A1
Ray and Chris
Plan for the night
Practice problems
Recurrence Analysis (Sp 15, MT1)
Indentation error: Everything should be
encapsulated by the if statement
Recurrence Analysis (Sp 15, MT1)
The while loop wi

CS 170
Fall 2016
Efficient Algorithms and Intractable Problems
Christos Papadimitriou and Luca Trevisan
Midterm 1
Name: Joe Solutions
SID: 12345678
GSI and section time:
Write down the names of the students on your left and right as they appear on their S

U.C. Berkeley CS170 : Algorithms
Lecturers: Sanjam Garg and Prasad Raghavendra
Second Midterm
Nov 5, 2015
Second Midterm Solutions
Name:
SID:
GSI and section time:
Read the questions carefully first. Be precise and concise. The number of points indicate t

CS 170
Fall 2016
Efficient Algorithms and Intractable Problems
Christos Papadimitriou and Luca Trevisan
Midterm 2
Name: Joe Solutions
SID: 12345678
GSI and section time:
Write down the names of the students on your left and right as they appear on their S

U.C. Berkeley CS170 : Algorithms
Lecturer: Christos Papadimitriou
Midterm 2
November 13, 2007
Midterm 2
Name / SID:
TA / Section:
Answer all questions. Read them carefully first. Be precise and concise. The number of points indicate
approximately the amou

d-separation: How to determine which variables are independent in a Bayes net
(This handout is available at http:/web.mit.edu/jmn/www/6.034/d-separation.pdf)
The Bayes net assumption says:
Each variable is conditionally independent of its non-descendants,

Bayesian Networks 3
D-separation
1
D-separation
Given a graph G, we would like to read
off independencies
The converse is easier to think about:
when does an independence statement
not hold?
Eg. when can X influence Y?
2
1
D-separation
When can X influ

Conditional independence and D-separation
Local semantics: Each node is conditionally independent of its non-descendants
given its parents
X
Y
Z
U
V
X
Y
Z
The local semantics provides a sufficient condition for
independence.
In the first example, X and Y

Linear time algorithm for computing a small biclique
in graphs without long induced paths
Aistis Atminas1 , Vadim V. Lozin2 , and Igor Razgon3
1
3
DIMAP and Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
[email protected]
2
DIMA

Lecture 18
Linear Programming
18.1
Overview
In this lecture we describe a very general problem called linear programming that can be used to
express a wide variety of different kinds of problems. We can use algorithms for linear programming to solve the m

Rob van Stee: Approximations- und Online-Algorithmen
Vertex Cover Problems
Consider a graph G = (V, E)
S V is a vertex cover if
cfw_u, v E : u S v S
minimum vertex cover (MIN-VCP):
find a vertex cover S that minimizes |S|.
1
Rob van Stee: Approximations-

CS 170, Midterm #1 Solutions, Spring 2000
CS 170 Spring 2000
Solutions and grading standards for exam 1
Clancy
Exam information
179 students took the exam. Scores ranged from 5 to 30, with a median of 16 and an average of 16.3. There
were 19 scores betwee

UC BerkeleyCS 170
Lecturer: Gene Myers
Midterm 2
November 9
Midterm 2 for CS 170
,
Print your name:
(last)
(first)
Sign your name:
Write your section number (e.g. 101):
Write your sid:
One page of notes is permitted. No electronic devices, e.g. cell phone

Modular Arithmetic
Graphs
Formal Limit Proof
Addition: O(n)
Multiplication: O(n2 ) (naive)
Multiplication: O(nlogn) (FFT)
Euclids Rule: gcd(x, y) = gcd(x mod y, y)
# of bits in xy = ylog2 x n2n
n n
2 n! nn
2
f: S T is 1-to-1 (injective) & onto (surjective