CS计算机代考程序代写 AI algorithm a Certificate r

a Certificate r
A tour ofcost at mostD

b Catterall
checks we didforftc

check that total costof
the four E D

claim G has a H C iff
we have a tour ofCort E n is G

a if There is a HC in G
Tour of art n in G

b if we have a Tourofcostnis G There will be
a HC is a

NP Completeproblems we knowof
3 SAT in deep set

Given a setof a items where

i

Decision version of
oil knapsack

as

hH

Cotidour 2 Castoff
costof initial tour 2 artyMST
coatof our approxSol Ez CostofMST
costof our approx Sol s centfoptitoon
This is a E approximation algorithm

General TSP

Theorem if P NP then for
any constant971 there isno polynomial time approximation
algorithm with approximation
ratio f for the general TSP

Plan we will assume thatsuch
an approximation algorithm
exists we will then use it to
solve the H C problem

Given an instanceofthe H C
problem on graph G we
will construct G as follows
o G has the same setnodes

as in G
o G is a fullyconnectedgraph
Edges in G that are also G
have a cost of 1otheredges in 0 have a

costof flu I I

I
y

senti

if G has a H Ccat ofopt.to or I v I s f w 1
if c has a tour of arts f Iv l

G has aH

f

ti is lengthofjob I

I

I I k
r

t

a EI
E

This is a z approximation

times
H H A 11 Hat

m resources

7 7 2tm

to Etna
ti f k T’t

Ti c

tj flat
Thi is a e 5

approximations

ateachstep we are placing 2 nodes
in the set Theopt so1
needs atleast oneof them

Q doo Y
ftp.n.o

o
0

i

Yes

RHSvector
coefficient
matrix unknowns

he

E t

rain

t

Cajon
O

O

O

ai is a decisionvariablefor
each no de e e V
ai 0 if s
ki I i E S

e f Ini t ai s l
ai ai

Minimize Swine

Subject to

Kitaj 21 force p
EE

mm

ooyrfoos

0

0

hkpfw

WC53_

ai’t o i f s

ri’t p i ES
r

Say Ss se f i e V i ni la
in

Say S is our approx So l

W S f 2 Ufp
we s w Cs
W S f 2 W S

This is a z approximation

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Before Lecture Notes – 14
Before Lecture Notes – 15