Workstation Selection
Arden University being a hub for online distance learning courses makes to fully depend on
computer technology. Consequently, students need to acquire computer devices ideal for their
academic purposes. As an institution, Arden Unive
Lecture 20
NP-Completeness II
20.1
Overview
In the last lecture, we defined the class NP and the notion of NP-completeness, and proved
that the Circuit-SAT problem is NP-complete. In this lecture we continue our discussion of NPCompleteness, showing the f
2SAT Notes
Let us now investigate some variants
of the SAT problem and see how
various parameters may affect the
complexity of a problem.
In particular, we study the 2SAT
problem and its optimization version.
2SAT Page 1
We can limit the number of literal
Traveling Salesperson Problem
NP-Completeness
You have to visit n cities
You want to make the shortest trip
How could you do this?
What if you had a machine that could guess?
Lecture for CS 302
Non-deterministic polynomial time
Deterministic Polynomial Ti
Prove that 2SAT is in P
Shobhit Chaurasia (11010179), Harshil Lodhi (11010121), Hitesh Arora (11010122)
We propose the following polynomial time algorithm to decide whether a given 2SAT expression is
satisfiable or not.
Consider a 2CNF formula with n vari
Question:
Is there a polynomial algorithm for solving 2-SAT?
Proposition 1 2SAT P.
Proof. Given a formula F on variables cfw_x1, x2, . . . , xn,
construct a directed graph G whose vertices are
cfw_x1, x2, . . . , xn, x1, x2, . . . , xn.
For every clause l
Answers for Homework 11
CIS 675 L Algorithms
(i) DPV Exercise 8.2.
(iii) DPV Exercise 8.4.
Suppose, given a graph G, the procedure D(G) re- (a) An instance of clique-3 consists of a graph G and
an integer k. A possible solution consists of a set
turns tru
CoNP and Function Problems
coNP
By denition, coNP is the class of problems
whose complement is in NP.
NP is the class of problems that have succinct
certicates.
coNP is therefore the class of problems that
have succinct disqualications:
A no instance of a
C
B
A
Our First NP-Complete
Problem
The Cook-Levin theorem
Compl
1
Introduction
Objectives:
To present the first NP-Complete
problem
Overview:
SAT - definition and examples
The Cook-Levin theorem
What next?
Compl
2
SAT
Instance: A Boolean formula.
Where Can We Draw The
Line?
On the Hardness of
Satisfiability Problems
1
Introduction
Objectives:
To show variants of SAT and check if
they are NP-hard
Overview:
Known results
2SAT
Max2SAT
2
What Do We Know?
Checking if a propositional calculus
for
2SAT
Instance: A 2-CNF formula
Problem: To decide if is satisfiable
Example: a 2CNF formula
(xy)(yz)(xz)(zy)
(xy)(yz)(xz)(zy)
Complexity
D.Moshkovits
1
PAP 184-185
2SAT is in P
Theorem: 2SAT is polynomial-time
decidable.
Proof: Well show how to solve t
1- A (network) is comprised of several linked computer systems exchanging and sharing data
and resources
1- New high-speed, all-digital packets-switching protocols are SMDS and (Asynchronous
Transfer Mode or ATM)
2- In a (star) topology, the network nodes
Department of Electrical Engineering, American University of Sharjah
ELE 353 Control Systems 1 - Quiz 2 (Solutions)
1. Provide a YES or NO answer to each of the following quiz questions. (3 points)
G(s)
R(s)
+
1
C(s)
+
(a)
R(s)
+
C(s)
G(s)
+
1
(b)
(a)
C(s
Q1. (20 points) Find
a)
b)
y (sin x) x cosh x
cos( y x) e
ex
x2 1
y sec ( x ) ln
x( x 2)(3 x 2 )
1
c)
dy
dx
2
1
Q2. (20 points)
Consider the function f ( x) x 2 x , x 1 .
a) Sketch the graph of f .
2
b) Show that
f
1
exists and determine its domain.
c) Fi
Circle the most accurate answer for each of the following:
1)
A survey of 30 emergency room patients found that the average waiting time
for treatment was 174.3 minutes.Assuming that the populatuion variance is
2162.25 (minutes ), the 95% confidence inter
1. Terms of contract?
2. what is Your responsibilities' when you sell goods?
3. What is organization?
4. Types of organizations and its aspects?
5. What is trust organization?
6. Types of corporations?
7. Dissolution of corporation?
8. Types of employment
Department of Mathematics & Statistics
October 21 2015
Calculus III (Math203)
NAME:
First Exam
(Allowed Time: 90 minutes)
ID#:
Key
Fall 2015
Section:
Instructions: Please read the following instructions before you start.
Do not open this exam until you ar
Midterm 2 Exam
Principles of Microeconomics
ECO 201
Date:
Semester:
Instructor:
Khusrav Gaibulloev
Instructions: This is a closed books and closed notes exam. You may use calculator that is nonprogrammable and without graphing function. For the problem so
Department of Mathematics and Statistics
MTH 103 - Calculus I
Final Exam - Fall 2012
Date: January 15, 2013
A
Time: 5:00-7:00pm
Circle your instructors name:
Dr. Taher Abualrub
Dr. Abdul Salam Jarrah
Dr. Dmitry Efimov
Dr. Suheil Khoury
Dr. Rim Gouia
Dr. I
Linear Models
Modeling is the process of writing a differential equation to
describe a physical situation. Almost all of the differential equations
that you will use in your study or in your job are there because
somebody, at some time, modeled a situatio
Quiz 1 (A)
ECO 201 Principles of Microeconomics, Fall 2014
Name:_
I.D:_
1. If all of the worlds resources were to magically increase a 100 times, then:
a. The scarcity principle would disappear.
b. Economics would no longer be relevant.
c. Tradeoffs would
Q1. (20 points) Find
a)
b)
y (sin x) x cosh x
cos( y x) e
ex
x2 1
y sec ( x ) ln
x( x 2)(3 x 2 )
1
c)
dy
dx
2
1
Q2. (20 points)
Consider the function f ( x) x 2 x , x 1 .
a) Sketch the graph of f .
2
b) Show that
f
1
exists and determine its domain.
c) Fi
Q1. (6 points) For each of the following equations, find
dy
dx
at the given points, if any.
y ( 3 ) x cosh( x 2 ) , x 0
a)
y log 2 x 4 1 , x 1
b)
c) y x x y
Q2. (8 points) Consider the function f ( x) x 3 1 . Determine whether the function is 1-1
or not.
Department of Economics, School of Business Administration
American University of Sharjah
Principles of Microeconomics
Quiz 3 Date: Wednesday, 23rd March 2016
Instructor: Dr. Javed Younas
NAME: _
ID:_
1. Use the graph below to answer questions A C:
A. Com
MTH203
Review Problems for EXAM#1
FALL 2015
Please note that this review does not cover all topics that will be on the exam. You must
study your notes from class and recitation, and do many exercises from the textbook. Also,
look at the chapter reviews in
Fall 2011 final exam
1. (10 points) Consider the following system
x + y + z = k
2x 3y + z = 2
y + kz = 6 + k
(a) Find all values of k so that the system has a unique solution.
(b) Find all values of k
1
2. (10 points) Let A = 1
1
so that the system has in
Q1. (14 points)
n 1
3n 1 n 1
a) Determine whether the sequence
i)
decreasing, increasing or neither,
ii)
bounded or unbounded,
iii)
converges or diverges.
(1) n n
b) Determine whether the sequence
converges or diverges.
n
e n 1
c) Evaluate the li
MTH203
Review Problems for Final(Line Integrals)
Fall 2013
Please note that this review does not cover all topics that will be on the exam. You must
study your notes from class and recitation, and do many exercises from the textbook. Also,
look at the cha
Department of Electrical Engineering
ELE441 Microelectronics
Fall 2007
Quiz #2 / 21 Oct 2007
Name:
ID:
(1) Drift current is where if there was a concentration gradient in carrier density, carriers
will flow from higher to lower regions of concentration, t