1. K-Depth Look-ahead Task Scheduling in Network of Heterogeneous Processors
Namyoon Woo and Heon Y. Yeom
School of Computer Science and Engineering
Seoul National University, Korea
{nywoo,

2. List Scheduling Heurstic
Introduction (1)
Problem Definition
Input
Task precedence graph (Directed weighted acyclic graph)
Processor-network graph
Objective
Minimizing the overall task execution time.
Satisfying the precedence order of tasks.
Before the run time.
NP-Complete problem
List Scheduling Heurstic
It is know as Cost-effective heuristic

3. Introduction (2) : List Scheduling
(3)
(1)
Time T4 T1 T2 T0 T1 T3 T4 T2 T0 T3 T0 T2 T1 T3
(2) T4 T0 P0 P1 P3 P2 T3 P0 P1 P3 P2 P0 P1 P3 P2

4. “Earilist Start Time” (EST) Earliest Finish Time” (HEFT)
Related Works (1)
“Earilist Start Time” (EST)
Homogeneous Processing
“Heterogeneous
Earliest Finish Time” (HEFT)
[topcuoglu99HCS]
Heterogeneous Processing Tx Ti Ty Tz … Tx Tx Ty Ty Ti Ti Ty Ty Ty Ty P0 P1 P2 P0 P1 P2

5. “Bubble Scheduling and Allocation” (BSA)
Related Works (2)
“Bubble Scheduling and Allocation” (BSA)
[kwok2000CC] Tx Tx Tx Tx Tx Ti Ti Ti Ti Ty Ty Ti Ti Ty Ty Ty Tz Tz Tz Ty Tz Tz Tz Tz P0 P1 P2 P3 P0 P1 P2 P3 P0 P1 P2 P3
pivot
pivot
pivot

6. Heterogeneous Network Links “Successor’s Expected Start Time” (SEST)
Motivation (1)
Heterogeneous Network Links
“Successor’s Expected Start Time” (SEST) T0 e1 e2 e3 e4 e5 Tx Ty Ti Ty Ty P0 T0 e1 e3 e2 e4 e5 P1 ? Tz P0 P1 P2

7. Clustering k successive tasks.
Motivation (2)
Clustering k successive tasks. T0 P0 P1 P2 T0 T3 T2 T4 T5 T6 T2 T3
K-depth T4 T’ T5 T6

8. k-Depth Look-ahead Heuristic
ID of Task X
ID of Processor K
Predefined Depth
w’(i,x)
Heterogeneous exe. Time of task i on Processor x
h’x
Average network cost of Processor x
c(i)
Average weight of out-edges from task i
SUCC(Ti)
A set of Task I’s successor tasks
NB(Px)
A set of neighbor processors of processor x

9. k-DLA Scheduling Heuristic
List the tasks in the pre-defined order
while the list is not empty do
Select the first task Ti and remove it from the list.
For all Px, calculate est(i,x) + ebl(i,x,k).
Select Px which gives the minimum value of the sum
Schedule Ti on Px
end while

10. Experimental Environment
Directed acyclic graphs
Random Graph
# of tasks (t ) : 50~900
# of edges = from 2t to 5t
Real Application
Stencil / LU-Decomposition / Laplace Transform
# of tasks : over 2000.
Processor network architecture
16 nodes –Ring / Mesh / Fully Connected Network
Variables
Heterogeneous Factor (HF) : 5, 10, 20, 40
Communication to Computation Ratio (CCR) : 0.1, 1, 10.0

11. Metrics for the Performance Comparison
Metircs
Normalized Schedule Length (NSL)
Schedule Length /  the weight of tasks on critical path
NSL shows how close to the optimum the scheduling result is.
Running Time
The cost of the scheduling heuristic itself
Used Processor
The tendency or locality of task-processor mapping
Heuristics
BSA, HEFT, k-DLA (k=1, 5, infinite)

12. Results (1) : Number of Tasks (CCR=1.0, HF=20)
Ring
Mesh
Clique
BSA
HEFT
1-DLA
5-DLA
-DLA

13. Results (2) : CCR (n=500, HF=20)
Ring
Mesh
Clique
BSA
HEFT
1-DLA
5-DLA
-DLA

14. Results (3) : Scheduling Time (CCR=1.0, HF=20)
Ring
Mesh
Clique
BSA
HEFT
1-DLA
5-DLA
-DLA

15. Results (4) : # of scheduled processors
Ring
Mesh
Clique
BSA
HEFT
1-DLA
5-DLA
-DLA

16. Results (5) : Conventional graph (CCR=1.0, HF=20)
LU 64
Stencil
Laplace

17. Analysis and Conclusions
Low
High
CCR
1-DLA
-DLA (except in clique) HF
Network Connectivity
-DLA
1-DLA or HEFT
The DLA heuristic with large k is suitable for the heterogeneous computing system where the network resource is expensive.
We can adjust the value k according to the characteristic of a given computing system.