CS270 Combinatorial Algorithms and Data Structures, Spring 2012
Problem Set 1
Due Date: Feb 2, 2012.
1. Given a graph, G = (V, E), and pairs (s1 , t1 ), . . . , (sk , tk ). we wish to find a set of paths connecting si and
ti . In class, we discussed the f
Last Updated: April 2, 2015
Due Date: April 16, 2015
CS270 Combinatorial Algorithms and Data Structures
Homework 2
You are allowed to discuss with others but not allowed to use any references except the course notes.
Please list your collaborators for eac
CS270 Combinatorial Algorithms and Data Structures
Homework 2 hints
Last Updated: April 9, 2015
Due Date: April 16, 2015
1. Extreme Point Solutions
(2) implies (1) is very easy.
For (3) implies (2), if you were in class, what Joseph said is the solution;
CS270 Combinatorial Algorithms and Data Structures
Homework 1 (complete)
Last Updated: Feb 19, 2015
Due Date: March 19, 2015
You are allowed to discuss with others but not allowed to use any references except the course notes and
the books Probability and
CSCI5450 Randomness and Computation
Homework 0: Warm-Up Exercises
Last Updated: Tue, Jan 4, 2010
1. Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin.
We repeatedly do the following: choose one ball from t
CS270 Combinatorial Algorithms and Data Structures
Homework 3 hints
Last Updated: May 4, 2015
Due Date: May 11, 2015
1. Bipartite Graphs
Use the Rayleigh quotient characterization of the first and the last eigenvalues. Compare them and
use Perron-Frobeniu
CS270 Combinatorial Algorithms and Data Structures
Homework 3
Last Updated: May 9, 2015
Due Date: May 11, 2015
You are allowed to discuss with others but not allowed to use any references except the course notes.
Please list your collaborators for each qu
CS270 Combinatorial Algorithms and Data Structures
Homework 1 hints
Last Updated: March 12, 2015
Due Date: March 19, 2015
1. Minimum k-cut
To lower bound the number of edges in the graph, one possible way is to sum over all possible trivial
k-cuts (i.e. k
Parallel Algorithms
Parallel computa2on is here!
During your career, Moores Law will probably
apply mostly to cores
Googles engine (reportedly) has about
500,000 processors (recall Map-Reduce)
Top supercomputers have
CS270 Combinatorial Algorithms and Data Structures, Spring 2016
Homework 3
Due: April 19 in class
Check Piazza for our homework policy. You can collaborate with at most three other students and must
write your own solution. List your collaborators on the
CS270 Combinatorial Algorithms and Data Structures, Spring 2016
Take-home Final
Due: 11:59pm, May 7 (Saturday). No extension will be granted.
Rules:
(a) Submit your solutions to [email protected], with CS270 Final as the title.
(b) Solve any 5 of the
Sex as an Algorithm:
The Theory of Evolution under the Lens of Computation
Adi Livnat
Christos Papadimitriou
Department of Evolutionary and Environmental
Biology, and Institute of Evolution
University of Haifa
Mount Carmel, Haifa 3498838, Israel
Computer
Chapter 12
Random walks, Markov chains,
and how to analyse them
Today we study random walks on graphs. When the graph is allowed to be directed and
weighted, such a walk is also called a Markov Chain. These are ubiquitous in modeling
many real-life settin
CS271 Randomness & Computation
Fall 2011
Lecture 24: November 22
Lecturer: Alistair Sinclair
Based on scribe notes by: Daniel Chen and Kaushik Ravindran
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications
Lecture 1 (27.02.2013)
Scribe: Lukasz Solak
Lecturer: Marek Cygan
Algebraic methods
1
Introduction
Presenting problems in terms of algebra leads to simple algorithms, in order to solve a problem
sometimes it is enough to check if determinant or rank of a
princeton univ. F13
cos 521: Advanced Algorithm Design
Lecture 2: Kargers Min Cut Algorithm
Lecturer: Sanjeev Arora
Scribe:Sanjeev
Todays topic is simple but gorgeous: Kargers min cut algorithm and its extension. It
is a simple randomized algorithm for fi
CS270 Combinatorial Algorithms and Data Structures, Spring 2016
Homework 1
Due: February 18 in class
Check Piazza for our homework policy. You can collaborate with at most three other students and must
write your own solution. List your collaborators on t
CS270 Combinatorial Algorithms and Data Structures, Spring 2016
Homework 2
Due: March 17 in class (except for the last problem)
Check Piazza for our homework policy. You can collaborate with at most three other students and must
write your own solution. L
U.C. Berkeley CS270: Algorithms
Lecturer: Christos Papadimitriou
Lecture 2-3
Last revised January 25, 2016
Lecture 2-3
1
The multiplicative weights update method
The multiplicative weights method is a very useful framework applicable to a wide variety
of
U.C. Berkeley CS270: Algorithms
Lecture 5
Lecturer: Christos Papadimitriou
Prev.Scribe: Anupam Last revised January 21, 2016
Lecture 5
1
Overview
We will discuss the first of two important applications of the expert framework: approximately solving zero s