0

In Introduction to Algorithms P657, 3rd edition, it says:

A critical path is a longest path through the dag, corresponding to the longest time to perform any sequence of jobs. Thus, the weight of a critical path provides a lower bound on the total time to perform all the jobs.

I understand the first sentence. But in the second sentence, it says

a critical path provides a lower bound

Why it provides a lower bound instead of a upper bound on the total time to perform all the jobs?

I think I might misunderstand critical path??

fuiiii
  • 1,359
  • 3
  • 17
  • 33
  • Because the assumption is being made that all tasks are performed in an optimal order, with maximum parallelization. As either of those assumptions is relaxed the total time to perform all jobs will increase. – Pieter Geerkens Dec 06 '15 at 15:59

1 Answers1

0

You can't start any job in the critical path before finishing the previous jobs in the path. So any legal schedule will take the sum of the weights to do all the jobs on the critical path. So any critical path is a lower bound on the time to do all of the jobs.

(the longest critical path would also be the time to complete all the jobs if you always had enough resources to work on all currently startable jobs at the same time).

mcdowella
  • 19,301
  • 2
  • 19
  • 25