SCHEDULING DAGs WITHOUT CONSIDERING

COMMUNICATION

Prepared by:

Afrah SalmanNoor Kadhim

Zeena Mohammed

SCHEDULING DAGs WITHOUT CONSIDERING

COMMUNICATION

• There are three polynomial algorithms:

1) Scheduling In-Forests/Out-Forests Task Graphs

2) Scheduling Interval Ordered Tasks

3) Two-Processor Scheduling

Requirements of the algorithms

• In the three cases, we assume the following:

• A task graph consists of n tasks;

• A target machine is made of m processors;

• The execution time of each task is one unit of

time;

• Communication between any pair of tasks is zero;

• The goal is to find an optimal schedule that

minimizes the total execution time.

Scheduling In-Forests/Out-Forests Task Graphs

Algorithm 1

1. The level of each node in the task graph is

calculated as given above, and used

as each node’s priority.

2. Whenever a processor becomes available,

assign it the unexecuted ready task

with the highest priority.

Example 1

Scheduling Interval Ordered Tasks

Algorithm 2

1. The number of all 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.

Example 2

Two-Processor Scheduling

Algorithm 3

1. Assign 1 to one of the terminal tasks.

2. Let labels 1, 2, . . . , j 2 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 L(y1), L(y2), . . . , L(yk) be the labels already assigned to the immediate successors of x. Then l(x) is the decreasing sequence of integers formed by ordering the set fL(y1), L(y2), . . . , L(yk)g. Let x be an element of S such that for all x0 in S, l(x) l(x0) (lexicographically). Assign j to x (L(x) ¼ j).

3. Use L(v) as the priority of task v and ties are broken arbitrarily.

4. Whenever a processor becomes available, assign it the unexecuted ready task with the highest priority. Ties are broken arbitrarily.

Example 3