Question
4. (3.4) Let d be the maximum degree of concurrency in a task-dependency graph with t tasks and a critical-path length l. Prove that [t/l]
4. (3.4) Let d be the maximum degree of concurrency in a task-dependency graph with t tasks and a critical-path length l. Prove that [t/l] d t l + 1. Note: [t/l] is meant to be the ceiling of t/l. Also note the equation contains both letter l and integer 1. This is trying set a relationship between the critical path length of a graph and maximum parallelism. For example, if the maximum parallelism is t (=number of tasks), then critical( path cannot be greater than 1. Likewise, if the maximum parallelism is 1, then the critical path must be at least t. You can use proof by contradiction.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started