35 pages
English
Le téléchargement nécessite un accès à la bibliothèque YouScribe
Tout savoir sur nos offres

# Inf2 Tutorial 4

-

Le téléchargement nécessite un accès à la bibliothèque YouScribe
Tout savoir sur nos offres
35 pages
English

Description

Sujets

##### Informatique

Informations

 Publié par Nombre de lectures 39 Langue English

Exrait

Inf2
Tutorial
Sharon
March
Sharon Wulﬀ
Wulﬀ
19,
4
2009
Inf2 Tutorial
4
Input identical machines; n jobs; job j has a process time: mtj
Job j must run contiguously on one machine. A machine can process at most 1 job at a time.
Def.Let a be a mapping function which assigns each job to one machine
a:{1, . . . , n} → {1, . . . , m}
ıa(ı)
Assumption.The number of jobs is larger than the number of machines
hSraonW
n > m
ulnIf2uTtorial4
Def.
Def.
Li=Xtk k:a(k)=i
1ixk:a(Xk)=i L= arg1miaxmLi ma= argm
SharonuWlnIf2uTotirla4
tk
Minimizethe total run time of all the jobs, In other words..
Assign each job to a machine such that theMaximalload is minimized(why?)
(Scary) Formulation used in the lecture,
a min= argH(a min) = arg{maxt 1ikm:a(Xk)=ik} a a
hSranouWlnI2fTutorial4
A Word On Mathematical Notation
a= arg minH(a min) = arg{1miaxkm:a(Xk)tk} a a =i
from right to left..
ranouWlnI2fuTot
k:a(k)=i
Xtk
a= arg minH(a min) = argtk} a{1miaxk:a(Xk)=i a m
A Word On Mathematical Notation
4lairout2TnfIulnWroha
Xtk
k:a(k)=i
is the load on the i’th machine.
ial4
A Word On Mathematical Notation
a m= argainH(a m) = argain{1miaxmk(Xk)=tk} :a i
A Word On Mathematical Notation
irlauTot
Xtk
k:a(k)=i
= arg minH(a) = arg min{maxmXt a1ik:a(k)=ik} a a
4
is the load on the i’th machine.
maxXtk 1imk:a(k)=i
A Word On Mathematical Notation
a a1iaxmXtk} a= arg minH(a min) = arg{m k:a(k)=i
Xtk
k:a(k)=i
is the load on the i’th machine.
ik:a(Xk)=i 1maxmtk
is taking the maximum load over allmachines(this is essentially L, themaximum load).
hSraonWulInf2Tutorial4
istathemkingapemblsifjsongpivomuminisopllareoamlmuximaumimin2fnIluWnorahS.d
Word
A
tk}
arg main{maxX 1imk:a(k)= i
4
II
On Mathematical Notation
rialTutonehias.stobacomoehtmitpissiylpmg.Themapalmappinhhsahtmeipgnhwci
A Word On Mathematical Notation II
is taking the minimum over all possiblemappings of jobs machines.
to
arg min{1miaxk:a(Xk)=itk} a m
2fuTlnIla4otirrahSuWnolmum.daoumimximathasinemgnhwcihhhTmepaipmapping.eoptimalhtylpmissia