15-451 Algorithms, Fall 2009
Homework # 6
due: Tue-Wed, November 17-18, 2009
Ground rules:
This is an oral presentation assignment. You should work in groups of three. At some point
before Sunday, No
15-451 Algorithms, Fall 2009
Homework # 4
Due: Tue-Wed, October 20-21, 2009
Ground rules:
This is an oral presentation assignment. You should work in groups of three. At some
point before Saturday, O
15-451 Algorithms, Fall 2011
Homework # 3
Due: October 11, 2011
Please hand in each problem on a separate sheet and put your name, andrew id, and
recitation (time or letter) at the top of each sheet.
15-451 Algorithms, Fall 2009
Homework # 2
due: Tue-Thu, September 22-24, 2009
Ground rules:
This is an oral presentation assignment. You should work in groups of three. At some
point before Saturday,
Midterm (version A)
15-451 Algorithms
Name:
Fall 2007
Section:
1
2
3
4
Total
43
20
21
16
100
One sheet of notes is allowed. Closed book.
1. Multiple Choice: circle the correct answer (43 pts)
For (a)-
15-451/651: Design & Analysis of Algorithms
Lecture #22 Sweep-Line and Segment Intersection
1
April 13, 2016
last changed: April 12, 2017
Preliminaries
The sweep-line paradigm is a very powerful algor
15-451/651: Design & Analysis of Algorithms
Lecture #18: Approximation Algorithms
March 28, 2017
last changed: March 26, 2017
While we have good algorithms for many optimization problems, the previous
15-451/651: Design & Analysis of Algorithms
Lecture #17
October 27, 2014
last changed: October 27, 2014
In the last lecture, we dened the class NP and the notion of NP-completeness, and proved
that th
15-451/651: Design & Analysis of Algorithms
Lecture #21 Computational Geometry Introduciton
1
April 11, 2017
last changed: April 10, 2017
Introduction
Computational geometry is the design and analysis
15-451/651: Design & Analysis of Algorithms
Lecture #25 Expert Advice
1
April 27, 2017
last changed: April 27, 2017
Prediction with Expert Advice
Today well study the problem of making predictions bas
15-451/651: Design & Analysis of Algorithms
Lecture #20
1
April 6, 2017
last changed: April 5, 2017
Mechanism Design (incentive-aware algorithms, inverse game theory)
How to give away a printer
The
15-451/651: Design & Analysis of Algorithms
Lecture #19: Powerful Arrays
1
April 4, 2017
last changed: April 4, 2017
Arrays with Super Powers
Today were going to take a break from abstract high-powere
Notes on Amortization
D. Sleator
1. Introduction
A data structure is a way of representing information in a computer and a set of procedures for accessing and updating the information. These procedure
15-451/651: Design & Analysis of Algorithms
Lecture #7: Union-Find and MSTs
September 17, 2014
last changed: September 16, 2014
In this lecture we describe the union-nd problem. This is a problem that
Lecture 14
Network Flow I
14.1
Overview
In these next two lectures we are going to talk about an important algorithmic problem called the
Network Flow Problem. Network ow is important because it can b
15-451/651: Design & Analysis of Algorithms
Lecture #2: Concrete models and tight upper/lower bounds
August 27, 2014
last changed: August 27, 2014
In this lecture, we will examine some simple, concret
15-451/651: Design & Analysis of Algorithms
Lecture #1: Introduction, and Median Finding
August 25, 2014
last changed: August 25, 2014
The purpose of this lecture is to give a brief overview of the to
15-451/651: Design & Analysis of Algorithms
Lecture #6
September 15, 2014
last changed: September 15, 2014
In the classic string matching problem, theres a string T of length t and a pattern P of leng
15-451/651: Design & Analysis of Algorithms
Lecture #9: Dynamic Programming II
September 24, 2014
last changed: September 23, 2014
In this lecture we continue our discussion of dynamic programming, fo
15-451/651: Design & Analysis of Algorithms
Lecture #8: Dynamic Programming I
September 22, 2014
last changed: September 19, 2014
Dynamic Programming is a powerful technique that allows one to solve m
October 20, 2014
15-451/651: Design & Analysis of Algorithms
Lecture #14: Linear Programming II
last changed: October 20, 2014
In this lecture discuss the general notion of Linear Programming Duality,
15-451/651: Design & Analysis of Algorithms
Lecture #14: Linear Programming I
October 15, 2014
last changed: October 14, 2014
In this lecture we describe a very general problem called linear programmi
15-451/651: Design & Analysis of Algorithms
Lecture #13: Game Theory
October 8, 2014
last changed: October 15, 2014
In todays lecture, well talk about game theory and some of its connections to comput
Lecture 15
Network Flow II
15.1
Overview
The Ford-Fulkerson algorithm discussed in the last class takes time O(F (n + m), where F is the
value of the maximum ow, when all capacities are integral. This
15-451/651: Design & Analysis of Algorithms
Lecture #23
April 18, 2017
last changed: April 16, 2017
Last time we looked at algorithms for finding approximately-optimal solutions for NP-hard problems.
15-451/651: Design & Analysis of Algorithms
Lecture #24 Closest Pairs
1
April 25, 2017
last changed: April 25, 2017
Preliminaries
Well give two algorithms for the following closest pair problem:
Given
15-451 Algorithms, Spring 2017
Recitation #7 Worksheet
Network Flow
Example of running Ford-Fulkerson: Here is a problem from the midterm in 2013.
Consider the graph below.
a
8
c
6
8
3
1
s
5
t
7
7
b
8
15-251: Great Theoretical Ideas in Computer Science
Notes on The Lambda Calculus (draft!)
1
15251 Staff
January 29, 2012
Syntax
Lambda expressions are defined recursively as follows:
Variable: a, b, c
15-451 Algorithms, Spring 2017
Recitation #10 Worksheet
Counting Axis-Aligned Segment Intersections
Youre given n vertical line segments in the plane and m horizontal ones. The problem is
to count the