1. Computer Science and Engineering Parallel and Distributed Processing CSE 8380 March 03, 2005 Session 15

2. Computer Science and Engineering Scheduling Review Optimal Algorithms without communication Interval Orders 2 Processors Communication Models Optimal Algorithms with communication Heuristics

3. Computer Science and Engineering Interval Orders A task graph is an interval order when its nodes can be mapped into intervals on the real line, and two elements are related iff the corresponding intervals do not overlap. For any interval ordered pair of nodes u and v, either the successors of u are also successors of v or the successors of v are also successors of u.

4. Computer Science and Engineering Scheduling interval ordered tasks 1. The number of successors of each node is used as each node’s priority 2. Whenever a processor becomes available, assign it the unexecuted ready task with the highest priority (complexity?)

5. Computer Science and Engineering Example

6. Computer Science and Engineering Two Processor Scheduling 1. Assign 1 to one of the terminal tasks. 2. Let labels 1,2,...,j-1 have been assigned. Let S be the set of unassigned tasks with no unlabeled successors. We next select an element of S to be assigned label j. For each node x in S define l(x) as follows: Let y1, y2,...,yk be the immediate successors of x. Then l(x) is the decreasing sequence of integers formed by ordering the set {L(y1), L(y2),..., L(yk)}. Let x be an element of S such that for all x' in S, l(x) ≤ l(x') (lexicographically). Define L(x) to be j. 3. Use L(v) as the priority of task v and ties are broken arbitrary. 4. Whenever a processor becomes available, assign it the unexecuted ready task with the highest priority. Ties are broken arbitrarily.

7. Computer Science and Engineering Example

8. Computer Science and Engineering Communication Models Completion Time Execution time Communication time Completion Time as 2 Components Completion Time from the Gantt Chart

9. Computer Science and Engineering Completion Time as 2 Components Completion Time = Execution Time + Total Communication Delay Total Communication Delay = Number of communication messages * delay per message Execution time  maximum finishing time of any task Number of communication messages  model A Model B

10. Computer Science and Engineering Number of communication Messages Given a task graph G = (V,E) and its allocation on m processors f, we use proc(v) to refer to the processor to which task v is assigned. Model A: number of messages =the number of node pairs (u,v) such that (u,v)belongs to E and proc(u) ≠ proc(v). Model B: number of messages =the number of processor- task pairs (P,v) such that processor P does not compute task v but computes at least one direct successor of v.

11. Computer Science and Engineering Completion Time from the Gantt Chart (Model C) Completion Time = Schedule Length This model assumes the existence of an I/O processor with every processor in the system Communication delay between two tasks allocated to the same processor is negligible. Communication delay is counted only between two tasks assigned to different processors

12. Computer Science and Engineering Example A 1 D 1 E 1 B 1 C 1 Assume a system with 2 processors

13. Computer Science and Engineering Models A and B Assume tasks A, B, and D are assigned to P1 and tasks C and E are assigned to p2 A B D P1 C E P2 Model A Number of messages = 2 Completion time = 3 + 2 Model B Number of messages = 1 Completion time = 3 + 1

14. Computer Science and Engineering Model C A B CD E Communication Delay P1P2 0 1 2 3 4

15. Computer Science and Engineering Optimal Algorithms with Communication Interval orders on n processors In-forests / out-forests on two processors Refer to the lecture and the chapter on scheduling for the details

16. Computer Science and Engineering Heuristics Discussion of Heuristics Examples Refer to the lecture and the chapter on scheduling for the details