Meta-Algorithms for Scheduling a Chain of Coarse-Grained Tasks on an Array of Reconfigurable FPGAs

Table 4

Four possible solutions to GPRM sample problem: The first row shows the initially empty configurations. The second row shows the FPGAs with their initially loaded tasks (with the cost of loading included in the cost column in Row 2). We describe the example in detail for Solution 1: The cost of Row 2 is 3 because 3 of the 5 empty FPGAs are loaded with tasks while the other 2 remain empty. The cost of reconfiguring Row 2 into Row 3 is 4 (four FPGAs go from loaded to empty or vice versa while FPGA 3 retains the same task C). The cost of reconfiguring Row 3 into Row 4 is 4 (again four FPGAs either go from loaded to empty or vice versa while FPGA 3 continues to retain task C). We ignore the cost of emptying out the FPGAs at the end, giving a total cost of 3+4+4=11. Solutions 3 and 4 are the best, each with a total cost of 6.

Solution 1						Solution 2						Solution 3						Solution 4
1	2	3	4	5	$	1	2	3	4	5	$	1	2	3	4	5	$	1	2	3	4	5	$
					—						—						—						—
A	B	C			3	A	B	C	C		4	A	B	C		C	4	A	B		C	C	4
		C	A	B	4	A	B	D	E	C	3	A	B	D	E	C	2	A	B	D	E	C	2
D	E	C			4						—						—						—
Total cost					11	Total cost					7	Total cost					6	Total cost					6