Lecture 21
CSE 331
Oct 23, 2009
Mid term and such like
At the END of the lecture, graded HW4+mid term and HW 6
IMPORTANT: Read blog post on mid term before coming to me
(sticky post till Monday)
Scheduling to minimize lateness
n jobs: ith job (ti,di)
At most one job at
any time
Schedule the n jobs: ith job gets interval [si,fi=si+ti]
Not the sum
Algo picks si
GOAL: Minimize MAXIMUM lateness
Lateness of job i, li = max(0,fi-di)
The Greedy Algorithm
(Assume jobs sorted by deadline: d1≤ d2≤ ….. ≤ dn)
f=1
For every i in 1..n do
Schedule job i from si=f to fi=f+ti
f=f+ti
Solving end of Semester blues
Term paper
Exam study
Party!
331 HW
Max lateness
=2
Project
0
0
Exam study
Party!
Monday
Tuesday
0
331 HW
Wednesday
2
0
P
Term paper
Thursday
Friday
Today’s agenda
Prove that the schedule output minimizes the maximum lateness
Two definitions for schedules
Idle time
Max “gap” between two consecutively scheduled tasks
Idle time =0
=1
Inversion
(i,j) is an inversion if i is scheduled before j but di > dj
i
j
f=1
i
j
For every i in 1..n do
Schedule job i from si=f to fi=f+ti
f=f+ti
What is the idle time and
max # inversion for
greedy schedule?