ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
September 27, 2012
Problem Set 1A- Due Wednesday, October. 3, 2012 5:15PM
This is a warmup HW problem to get everyone started thinking about algorithms. For this problem
only you ar

HW 2 Solutions
Saturday, October 6
Dr. Charles Martel
ECS 222A, Fall 2012
Problem 1:
Our graph has n + 1 nodes numbered 0, 1, 2, . . . n, a dummy start node and one for each point. An arc
from node i to node j will represent a line that includes nodes i +

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
October 2, 2012
Problem Set 2 Due October. 11, 2012 11:55PM
Guidelines for writeups
When describing an algorithm rst give a high level overview of your approach, then ll in details

HW 1
Due Monday, October 10
(22) Problem 1.
Dr. Charles Martel
ECS 222A, Fall 2006
a. Construct a new graph H with vertex set V and edge set
b
E (H ) =
E ( Gi )
i=0
Then, we can simply use a breadth-rst search to nd the shortest path in H from s to
t in t

Homework 2 solutions - ECS222a F2006
October 26, 2012
1
Problem 1: Testing Communication Lines
A) We can solve the problem of testing communication lines by constructing a graph as described below,
and then applying a network ow algorithm. Create a node f

ECS 222A: Algorithm Design and Analysis
UC Davis | Tao Jiang
October 18, 2012
Homework Writeups
(22) Problem 1. Problem 14 in chapter 6 on page 324. Also, give the run time of your
solutions.
Solution:
A) First, we should build a graph G' with the same no

Scribe notes
VaZirani class
Lecture #7 (Tuesday7 September 16)
1 The problem
We use the ﬁnite ﬁeld Z73. For :1:7 y E Z2, :1: —|— y denotes the bitWise addition
and :1: - y denotes the inner product (2 wiyimodZ).
Input for Simon’s algorithm is a reversible

Local Search Algorithms
ECS 222A
Fall 2015
1
Coping With NP-Hardness
Q. Suppose I need to solve an NP-hard problem. What should I do?
A. Theory says you're unlikely to find poly-time algorithm.
Must sacrifice one of three desired features.
Solve problem t

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
January 13, 2012
Problem Set 1- Due January. 24, 2012 4:10PM
Guidelines for writeups
When describing an algorithm rst give a high level overview of your approach, then ll in details

Coping With Intractability
ECS 222A
Fall 2015
1
Coping With NP-Completeness
Q. Suppose I need to solve an NP-complete problem. What should I do?
A. Theory says you're unlikely to find poly-time algorithm.
Must sacrifice one of three desired features.
Solv

Approximation Algorithms
ECS 222A
Fall 2015
1
Approximation Algorithms
Q. Suppose I need to solve an NP-hard problem. What should I do?
A. Theory says you're unlikely to find a poly-time algorithm.
Must sacrifice one of three desired features.
Solve probl

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
September 24, 2009
Sample Homoework writeups
1
Find the missing Int
[25 points]
Problem 4-2 (Cormen, Leserson and Rivest), nd the missing int: We are given an array A with
n = 2k 1

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
October 24, 2015
Problem Set 3 Solutions
Problem 1. The yes/no clique problem is: given an undirected graph G=(V,E) and a target
integer k, is there a clique of size k? A clique is a set of

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
Dec. 4, 2015
Problem Set 6 Solutions
Problem 1. K&T 12.4.
a) Consider a progress measure dened as the sum of the squares of the loads on all
machines. We claim that after an improving swap m

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
Nov. 24, 2015
Problem Set 5 Solutions
(20) Problem 1.
a) Give an integer programming (IP) formulation for MAX-CUT. Prove that it is
equivalent to MAX-CUT.
There are several ways to do this;

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
November 12, 2015
Problem Set 4 Solutions
Problem 1: KT 10.1, Hitting Set This solution will be similar to the algorithm for Vertex
Cover from chapter 10.1. Consider the problems notation. F

Problem Set 2 Solutions
October 21, 2015
1
Problem 1: Negative cycles and Bellman-Ford
A best path of length i has some rst arc (v, w) and if we already have M [w] d [i 1, w] at the end of the
prior iteration (by induction), during the current iteration w

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
October 6, 2015
Problem Set 1 Solutions
Problem 1: Segmented Least Squares
Our graph has n + 1 nodes numbered 0, 1, 2, . . . n, a dummy start node and one for each point. An arc from
node i

ECS 222A: Algorithm Design and Analysis
UC Davis Vladimir Filkov
October 27, 2015
ECS 222 Midterm Exam
NAME:
ID:
Instructions: This is a closed book, open notes exam. No electronic devices may be used. Communicate your ideas clearly and
succinctly . Show

Algorithm Design and Analysis
Lectures 3 and 4
ECS 222A
Fall 2015
1
6.7 Sequence Alignment in Linear Space
Sequence Alignment: Linear Space
Q. Can we avoid using quadratic space?
Easy. Optimal value in O(m + n) space and O(mn) time.
Compute OPT(i, ) from

Algorithm Design and Analysis
ECS 222A
Fall 2015
1
Problems: Specific Statements of What to Solve
Algorithms: TMs
- Solutions
- precise enough (in pseudocode)
- finite
- correct
- efficient
Model of Computation:
- RAM
- Arithmetic operations, etc.: O(1)
E

Algorithm Design and Analysis
ECS 222A
Fall 2015
1
Problems: Specific Statements of What to Solve
Algorithms: TMs
- Solutions
- precise enough (in pseudocode)
- finite
- correct
- efficient
Model of Computation:
- RAM
- Arithmetic operations, etc.: O(1)
E

CS 222A Fall 2012, HW 6 Due Tuesday November 27, 2012
I think most of these problems are pretty simple, so if you get into something really elaborate, you probably are on the wrong path.
1. The LCP problem is the following: input is a set of k strings S1

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
October 3, 2012
Problem Set 1A SolutionsProblem 1.(20) Answer to a Pancake problem. The goal was to nd an algorithm that uses at
most 2n 4 ips in the worst case. Before proceeding,

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
October 11, 2012
Problem Set 3Due Friday, October 19 11:50PM
(22) Problem 1. Problem 14 in chapter 6 on page 324. Also, give the run time of your solutions.
(12) Problem 2. Problem

ECS 222A: Algorithm Design and Analysis
UC Davis Charles Martel
Handout ?
October 18, 2012
Problem Set 4Due Friday , October 26, 11:55PM
No late days for this assignment. All must be turned in by Friday
(25) Problem 1. Use network ows to nd an ecient solu

CS 222 Fall 2012 HW 5, Due Tuesday Nov. 13
Question 0 concerns hashing, presented by Professor Martel.
The remaining problems concern material on randomized algorithms.
Questions 1 and 2 can be done with only the material from Section 13.2,
discussed in c