Numerical on Longest Path Matrix (LPM) Algorithm

1. Numerical on Longest Path Matrix Algorithm By : Alisha Shahare

2. Q . For the DFG shown in figure . Compute the iteration bound ofthis DFG using LPM algorithm.

3. Solution :Let d be number of delays in DFG . Here there are two delays . = longest computation time of all paths from and that pass through exactly m-1 delays = -1 , if no path exist Here m =1,2 because there two delays in given figure . L=

4. For m=1 : for (i.e d1 to d1) path : d1—4– 5—6—d1 At every node there is unit time assign as shown in figure as (1) for addition and (2)for multiplication . Therefore , 1u.t +2u.t+1u.t= 4u.t i.e = 4

5. Similarly, for (i.e d1 to d2), path :d1—4– 5—7—d2 for (i.e d2 to d1), path :d2—1—2—3—4—5—6—d1 for (i.e d2 to d2), path :d2—1—2—3—4—5—7—d2 From above, = 4 , = 4 , = 8 , = 8

6. Therefore , For m=2 , = Where K is set of integer k in interval [1,d]such that neither nor holds value

7. For For

8. For For Therefore ,

9. Now we get and (consider diagonal element for iteration bound) Iteration bound is = {} = {, } = {, , , } = 8

10. Thank You