CME 192
Assignment 1: Calculating the eigenvalues of a matrix
Due: October 12, 2017 before class.
Overview:
Eigenvalues are important numbers associated with linear systems of equations.
Eigenvalues h
CME 323 Midterm Solutions
May, 2016
Problem 1
(15 points) Consider scheduling a sequence of jobs J1 , J2 , . . . , Jt on m machines. We wish to
minimize the time it takes for the heaviest loaded machi
CME 305: Discrete Mathematics and Algorithms
The following lecture notes are based heavily on the paper by Spielman and Srivastava, sometimes following
it literally.
1
Introduction
The goal of sparsif
CME 305: Discrete Mathematics and Algorithms
1
Computation and Intractability
In this series of lecture notes, we have discussed several problems for which there exist polynomial time
algorithms for p
CME 305: Discrete Mathematics and Algorithms
Instructor: Reza Zadeh ([email protected])
HW#2 Due at the beginning of class Thursday 02/09/17
1. (Kleinberg Tardos 7.27) Some of your friends with jobs
CME 305: Discrete Mathematics and Algorithms
Instructor: Reza Zadeh ([email protected])
HW#3 Due at the beginning of class Thursday 03/02/17
1. Consider a model of a nonbipartite undirected graph in
CME 305: Discrete Mathematics and Algorithms
Instructor: Reza Zadeh ([email protected])
Final Review Session 03/20/17
1. Let G = (V, E) be an unweighted, undirected graph. Let 1 be the maximum eigenv
CME 305: Discrete Mathematics and Algorithms
Instructor: Reza Zadeh ([email protected])
HW#1 Due at the beginning of class Thursday 01/26/17
1. Prove that at least one of G and G is connected. Here,
Discrete Mathematics and Algorithms
June 2015
Qualifying Exam
1. (10 points) Consider a graph G on 2n vertices where every vertex has degree at least
n. Prove that G contains a perfect matching.
2. (2
Discrete Mathematics and Algorithms Qualifying Exam
September 2015
1. (10 points) Prove that a graph with 2n nodes and minimum degree n must be connected.
2. (15 points) The problem of maximum clique
Discrete Mathematics and Algorithms
June 2016
Qualifying Exam
1. (15 points) Prove that a tree T has a perfect matching if and only if for every vertex
v the graph T v has exactly one odd component (a
Discrete Mathematics and Algorithms
June 2014
Qualifying Exam
1. (10 points) Show that every graph on m edges has a subgraph on at least m/2 edges
which is bipartite.
2. (15 points) The hypercube grap
Discrete Mathematics and Algorithms Qualifying Exam
September 2014
1. (10 points) A vertex cover of a graph is a subset C of the vertices such that each edge of
the graph is incident to at least one v
Discrete Mathematics and Algorithms
September 2016
Qualifying Exam
1. (10 points) Let X be a non-negative random variable with expectation E[X] = 0
and variance 2 . Prove that for all > 0,
+ 2
P r[X
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#3 - Due at the beginning of class May 18th.
1. Download the following materials:
Slides: http:/stanford
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#3 - Due at the beginning of class May 18th
1. Download the following materials:
Slides: http:/stanford.
CME 192
Assignment 1
Due: October 11, 2016
10:00am
Introduction
Eigenvectors and eigenvalues come up in many very different contexts and if you arent already familiar
with them, you probably soon will
function C = f_matMult(A,B,type)
%C = f_matMult(A, B, type)
%This function will multiply two matrices, element wise or matrix wise
%
%Input: A, B - matrices to be multiplied
%
type - a string containi
%Test script for the function f_matMult
% Test element-wise multiplication
%cfw_
%Define two matrices
A = rand(5,6);
B = rand(5,6);
%Call function
C = f_matMult(A,B,'elem');
%Check result again Matlab
CME 192: Introduction to Matlab
Stanford University, Fall 2016
Basic course information
Instructor: Anna Craig
Email: [email protected]
Dates: Tuesdays & Thursdays, September 29 October 25, 2016
Ti
CME 323: Distributed Algorithms and Optimization, Spring 2015
http:/stanford.edu/~rezab/dao.
Instructor: Reza Zadeh, Matroid and Stanford.
Lecture 18, 5/25/2016.
Landreman.
Scribed by Vishakh Hegde, A
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#4 - Due 5/25
1. Consider solving connected components via the Pregel framework. In general the naive
alg
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#1 Solution
1. The Karatsuba algorithm multiplies two integers x and y. Assuming each has n bits
where n
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#2 Due at the beginning of class April 27th
1. List Prefix Sums As described in class, List Prefix Sums i
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#2 Due at the beginning of class April 27th
1. List Prefix Sums As described in class, List Prefix Sums i
CME 323: Distributed Algorithms and Optimization
Instructor: Reza Zadeh ([email protected])
HW#1 Due at the beginning of class April 11th
1. The Karatsuba algorithm multiplies two integers x and y. A
CME 323: Distributed Algorithms and Optimization, Spring 2015
http:/stanford.edu/~rezab/dao.
Instructor: Reza Zadeh, Matroid and Stanford.
Lecture 9, 4/25/2016. Scribed by Max Bodoia, Erik Burton, and