Input: K: Number of the last fragment

Rmax: Number of database relations

Nmax: Number of fragments in each relation

Step 1: Set 0 to K

Step 2: Set 1 to R

Step 3: Do steps (4 - 21) until R > Rmax

Step 4: Set 1 to I

Step 5: Do steps (6 - 20) until I > Nmax

Step 6: Set 1 to J

Step 7: Do steps (8-18) until J > Nmax

Step 8: If I ¹ J and S_i ,S_j Є S_R go to step (9)

Else Add 1 to J, go to step (18)

Step 9: If S_i ∩ S_j ≠ Ø do steps (10)-(17)

Else, Add 1 to J and go to step (19)

Step 10: Add 1 to K

Step 11: Create new fragment F_k = S_i ∩ S_j and add it to F

Step 12: Create new fragment F_k+1 = S_i - F_k and add it to F

Step 13: Create new fragment F_k+2 = S_j - F_k and add it to F

Step 14: Delete S_i

Step 15: Delete S_j

Step 16: Set Nmax + 1 to J

Step 17: End IF

Step 18: End IF

Step 19: Loop

Step 20: Add 1 to I

Step 21: Loop

Step 22: Set 1 to I

Step 23 Do steps (24 - 35) until I > Nmax

Step 24: Set 1 to J

Step 25: Do steps (26 - 33) until J > Nmax

Step 26: If I ¹ J and S_i, S_j Є S_R go to step (27)

Else Add 1 to J, go to step (33)

Step 27: If S_i ∩ S_j = Ø do steps (28)-(33)

Step 28: Add 1 to K

Step 29: Create new fragment F_k = R_j - UF

Step 30: End IF

Step 31: If F_k ≠ Ø Add F_k to the set of F

Step 32: End IF

Step 33: Loop

Step 34: Add 1 to I

Step 35: Loop

Step 36: Set 1 to I

Step 37: Do steps (38 - 53) until I > F

Step 38: Set 1 to J

Step 39: Do steps (40 - 51) until J > F

Step 40: If I ¹ J and F_i, F_j Є F_R go to step (41)

Else, Add 1 to J and go to step (50)

Step 41: If F_i ∩ F_j ≠ Ø do steps (42)-(49)

Else, Add 1 to J and go to step (49)

Step 42: Add 1 to K

Step 43: Create new fragment F_k = F_i ∩ F_j and add it to F

Step 44: Create new fragment F_k+1 = F_i - F_k and add it to F

Step 45: Create new fragment F_k+2 = F_j - F_k and add it to F

Step 46: Delete F_i

Step 47: Delete F_j

Step 48: Set F + 1 to J

Step 49: End IF

Step 50: End IF

Step 51: Loop

Step 52: Add 1 to I

Step 53: Loop

Step 54: Add 1 to R

Step 55: Loop