computer science and engineering parallel and distributed processing cse 8380 march 03, 2005 session...

Computer Science and Engineering

Parallel and Distributed ProcessingParallel and Distributed Processing

CSE 8380CSE 8380

March 03, 2005March 03, 2005

Session 15Session 15


Scheduling

Review Optimal Algorithms without communication

Interval Orders 2 Processors

Communication Models Optimal Algorithms with communication Heuristics


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.


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?)


Example

0 0 0

3 2 1

4 5 61

9

1 1

1 1 1

1 1 1

1 2 3

654

7 8

Time P1 P2

123

4 5 6

87 9

P30

1

2

3


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.


Example2 1

4

1

5 1

6 1

7 1

8

1

1

1

9

1

10

111

1

15

1

13

13

1

12

114

1

16

1

17

1

12 3

4 56

78 910

11 12

13

14

15 16 17

1

3

4

2

5

67

16

9

10

11

12

15

8

17

13

14

P1 P2time


Communication Models

Completion Time Execution time Communication time

Completion Time as 2 Components Completion Time from the Gantt Chart


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


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.


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


Example

A

1

D

1

E

1

B

1

C

1

Assume a system with 2 processors


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


Model C

A

B

C D

E

Communication Delay

P1 P20

1

2

3

4


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


Heuristics

Discussion of Heuristics Examples

Refer to the lecture and the chapter on scheduling for the details

computer science and engineering parallel and distributed processing cse 8380 march 03, 2005 session...

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