| Operator Symbol | Operation | Memory buffer requirement | # Disk I/O operations |
|---|---|---|---|
| σC(R) | selection | M ≥ 1 | B(R) |
| πattrs(R) | projection | M ≥ 1 | B(R) |
| δ(R) | duplicate elimination | M ≥ B(R) (need hash index) | B(R) |
| γL(R) | grouping | M ≥ B(R) (hash on grouping attrs) | B(R) |
| R ∪ S | Union | M ≥ B(S) + 1 (hash on all attrs) | B(R) + B(S) |
| R ∩ S | Intersection | M ≥ B(S) + 1 (hash on all attrs) | B(R) + B(S) |
| R − S | Difference | M ≥ B(S) + 1 (hash on all attrs) | B(R) + B(S) |
| R ⋈ S | Join | M ≥ B(S) + 1 (hash on join attrs) | B(R) + B(S) |
| R × S | Product | M ≥ B(S) + 1 (store entire S in memory) | B(R) + B(S) |