CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 5 Sep 18, 2014
Prof. David Kirkpatrick
Scribe: Tingting Zhao
In this lecture we discussed:
Integer Multiplication
Polynomial Multiplication
Coecient representation
Point-value repres
Assignment 2: Sample solutions and comments
1. (a) In general the cost of a divide-and-conquer algorithm can be expressed
as the sum of three terms: the split cost (the cost of splitting the
problem into subproblems), the recursive cost (the cost of recur
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 1 September 04, 2014
Prof. David Kirkpatrick
Scribe: Nowrin Anwar Joyita
In this lecture we discussed:
Greatest Common Divisor;
Naive Algorithm for computing GCD;
Euclids Algorithm
Assignment 5: Sample Solutions
1. (a) Suppose that the edge colours are labeled 1, . . . c. We can transform
in out
the graph G by replacing each vertex v by 2c vertices, vj , vj , for
in
1 j c, and each edge (u, v) with colour j by the edge (uout , vj )
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 3 September 11, 2014
Prof. David Kirkpatrick
Scribe: Marjan Alavi
The discussed topics for this lecture are:
Chinese remainder theorem;
Eulers theorem;
RSA cryptosystem.
1
Claricati
Assignment 3: Sample solutions and comments
1. (a) Following the hint, we start by designing an algorithm whose search
cost, when the algorithm returns index i, is proportional to lg(1 + i).
(This essentially treats the special case when (j 1) = 1.) With
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 2 Sept 09, 2014
Prof. David Kirkpatrick
Scribe: Yu Ju (Edwin) Chen
In this lecture we:
Discussed the Euclid algorithm;
the extended Euclid algorithm;
modular inverses
Handouts (post
Assignment 4: Sample Solutions
1. The data structure developed in this question corresponds to the static
version of a more general structure presented in the paper:
Bose, P., Douieb, K., Dujmovic, V., Howat, J. and Morin, P., Fast local
searches and upda
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 6 Sept. 23, 2014
Prof. David Kirkpatrick
Scribe: Yuan Wang
In this lecture we discussed:
Fast Fourier Transforms;
ecient representation transforms (evaluation and interpolation) by c
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 7 Sept. 25, 2014
Prof. David Kirkpatrick
Scribe: Kailang Jiang
In this lecture we discussed:
Finding extrema of a set of n elements;
nd the maximum
nd the minimum
other problems reduc
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 15 October 23, 2014
Prof. David Kirkpatrick
Scribe: Zainab Zolaktaf
In this lecture we:
Discussed the Selection problem:
QuickSelect - a randomized algorithm ;
SampleSelect - a rand
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 11 Oct. 09, 2014
Prof. David Kirkpatrick
Scribe: Weihua Zhang
In this lecture we discussed:
construction of perfect hash functions (cont.);
A dynamic two-level hash scheme:
how can w
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 16 Oct 28, 2014
Prof. David Kirkpatrick
Scribe: Tobias K
In this lecture we:
Reviewed the SampleSelect algorithm;
Discussed a lower bound for the Selection problem;
Started the new
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 10 October 07, 2014
Prof. David Kirkpatrick
Scribe: Alireza Zakeri-Hosseinabadi
In this lecture we discussed:
Hash tables
Randomness in the design and analysis of hashing
Properties
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 9 October 2, 2014
Prof. David Kirkpatrick
Scribe: Oliver Schneider
In this lecture we:
used space to reduce update and search time for dictionaries,
looked at a direct access table a
CS500: Fundamentals of Algorithm Design and Analysis
Fall 2014
Lecture 8 - September 30, 2014
Prof. David Kirkpatrick
Scribe: Ehsan MohyedinKermani
Let S contains n inputs drawn from the universe U = cfw_0, 1, 2, , m 1.
Claim 1. In comparison model of com