[PDF] - The problem If one or more philosophers try to to e at PDF Document

SLIDE 1

The

problem If

ne
r

more philosophers try to to e at then

ne
f

them ev en tually after a nite time succeeds No Deadlo c k The ab

v

e prop ert y do es not pro vide an y guaran tee

n

an individual basis since a pro cessor ma y try to eat and y et fail since it alw a ys b ypassed b y

ther

philosophers What w e w

uld

lik e to ha v e is a stronger prop ert y

whic

h implies no deadlo c k No Starv ation If a philosopher wishes to eat then it will ev en tually after a nite time succeed as long as no philosopher k eeps eating forev er W e assume that eac h philosopher eats for at most

time

units

DS

I I L Philippas Tsigas

SLIDE 2

Symmetry

W e sa y that a solution to a distributed problem is symmetric if

all

pro cesses are iden tical nothing that distinguishes

ne

computer from the

ther
all

pro cesses run the same co de

all

shared

r

lo cal v ariables ha v e the same input v alue DS I I L Philippas Tsigas

SLIDE 3

Imp
ssibilit

y Result There is no symmetric solution to the dinning philosophers problem Pro

f

Assume for the purp

se
f

con tradiction that there is a solution A Consider a roundrobin execution

f

A in whic h rst philosopher p

mak

es its rst step then p

then

p n

W

e can pro v e b y induction that after this rst round all philosophers are going to b e in the same state and all links are going to ha v e the same messages No w w e can pro v e again b y induction

n

the n um b er

f

rounds that at the end

f

eac h round all philosophers are alw a y going to b e in the same state The last

ne

means that if philosopher p i at some p

in

t starts eating its neigh b

urs

will start eating together with him b y the end

f

the resp ectiv e round Contr adiction Accessible common resources are referred n y the pro cesses with their lo cal DS I I L Philippas Tsigas

SLIDE 4

names

DS I I L Philippas Tsigas

SLIDE 5

Righ

tLeft DP Proto col F

r

simplicit y n is ev en W e giv e dieren t proto cols to the philosophers

ne

for the philosophers that w e call with

dd

indices and

ne

for those with ev en indices The basic strategy is v ery simple Oddnumb er e d philosophers seek their righ t fork rst Evennumb er e d philosophers seek their left fork rst A philosopher seeks a c hopstic k b y putting its id at the end

f

that c hopstic ks queue The philosopher

btains

the c hopstic k when its index reac hes the fron t

f

that c hopstic ks queue When a philosopher nishes eating it returns b

th

c hopstic ks b y remo ving its index from their queues DS I I L Philippas Tsigas

SLIDE 6

Time

Complexit y IDEA A c hopstic k b et w een t w

philosophers

is either the rst c hopstic k for b

th
r

the second c hopstic k for b

th

Time Complexit y Roughly

DS

I I L Philippas Tsigas

SLIDE 7

Same

co de to the pro cesses Y

u

can ask from y

ur

system philosophers to get unique names from the range n

But

this is not going to b e lo c al b ecause the philosophers ha v e to learn n Y

u

can ask from y

ur

pro cesses to get a color from the set

f

colours P

f

bl ack

w

hite g so that no t w

neigh

b

urs

get the same color Can this b e done DS I I L Philippas Tsigas

SLIDE 8

Dinning

Philosophers Cn t W e can ha v e a solution to the dinning philosophers problem if w e start with a Black

White

coloring

f

the ring The Black

White

coloring can b e seen as a prepro cessing phase though that need to b e done from the system when philosophers lea v e the table

r

new

nes

are joining On aver age if b et w een t w

coloring

phases pro cesses sp end time prop

rtional

to n at the table

DS

I I L Philippas Tsigas

SLIDE 9

Philosophers

vs Chopstic ks Let us ha v e lo

k

at the algorithm that w e describ ed in the previous lecture The algorithm lo

k

ed lik e this

Hungry
Get

a Black

White

color if y

u

do not ha v e

ne
If

y

u

are Black seek righ t c hopstic k rst

if

y

u

are White seek left c hopstic k rst

After

nish eating put the c hopstic k bac k DS I I L Philippas Tsigas

SLIDE 10

Philosophers

vs Chopstic ks Cn t A new algorithm

Hungry
Giv

e a Black

White

consisten t color to y

ur

c hopstic ks if y

u

ha v e not done that

Seek

Black c hopstic k rst Remem b er The ide a

f

the rst algorithm w as that a c hopstic k b et w een t w

philosophers

is either the rst here blac k c hopstic k for b

th
r

the second here white c hopstic k for b

th

DS I I L Philippas Tsigas

SLIDE 11

Ho

w do I color c hopstic ks DS I I L Philippas Tsigas

SLIDE 12

Resource

Allo cation Generalising the Dinning Philosophers A resource allo cation problem consists

f

a nite set

f

r esour c es and some comp eting pr

c

esses Pro cesses request access to the resources from time to time in

rder

to execute a co de segmen t called critic al se ction Up

n

b eing gran ted all the requested resources a pro cess pro ceeds to use them and ev en tually relinquishes them Requiremen ts

Mutual

exclusion No resource should b e accessed b y more than

ne

pro cess at the same time

No

Starv ation As long as pro cesses do not fail no pro cess should w ait forev er for requested resources DS I I L Philippas Tsigas

SLIDE 13

Resource

Allo cation Solution W e generalise in a straigh tforw ard w a y the Righ tLeft Dinning philosophers algorithm to an arbitrary resource allo cation problem W e rst construct the Resource Graph

The

no des

f

this graph represen t the resources

There

is a no de from

ne

no de to another if there is some pro cess that uses b

th

the resources DS I I L Philippas Tsigas

SLIDE 14

Coloring

again W e no decolor the r esour c e gr aph DS I I L Philippas Tsigas

SLIDE 15

The

Generalisation Eac h pro cess seeks its resources in increasing

rder

according to the total

rdering

constructed b y the coloring A pro cess seeks a resource b y putting its index at the end

f

that resources queue The pro cess

btains

the resource when its index reac hes the fron t

f

that resources queue When a pro cess exits C it returns all

f

its resources b y remo ving its index from their queues Let us assume that k is the maxim um n um b er

f

pro cesses that require an y single resource What is the time complexit y

f

the algorithm DS I I L Philippas Tsigas