| Procedure GRA (, D, , TOL, ) |
| INPUT: the number of channels , the database D, the sorted access pattern , |
| the tolerance TOL, the maximal number of iterations . |
| OUTPUT: the near-optimal solution to WTM. |
| Step 1 Calculate , , and construct corresponding , ; |
| Construct the dummy objective function ; |
| Set ; . |
| Step 2 While () do Steps 3–15. |
| Step 3 Set ; ; . |
| //Note that is the Euclidean distance of . |
| Step 4 If () then |
| Output “”, “Zero gradient!”; |
| Stop. |
| Step 5 Set ; ; ; . |
| Step 6 While ) do Steps 7 and 8. |
| Step 7 Set ; . |
| Step 8 If () then |
| Output “, ”, “No more improvement!”; |
| Stop. |
| Step 9 Set ; . |
| Step 10 Set ; ; . |
| //Note that we use Newton’s forward divided-difference formula [11] to find a quadratic |
| //polynomial which interpolates at , , . |
| Step 11 Set ; . |
| //Note that the critical point of occurs at . |
| Step 12 Find from so that . |
| Step 13 Set . |
| Step 14 If () then |
| Set ; |
| Output “, , ”, and “Success!”; |
| Stop. |
| Step 15 Set . |
| Step 16 Output “, ”, “Maximum iterations exceeded!”. |
| Stop. |
