Choose position
When absolute slots carry meaning, as in schedules with strong stage or locus effects.
Shared representation · COIN + ROSE
Order
Schema
The same permutation can reveal different building blocks. COIN and ROSE differ not because one sees another solution, but because each chooses a different relation to learn.
ADBEC
| Schema | Question learned | Example | Algorithm family |
|---|---|---|---|
| Position | Which item tends to occupy locus k? | pos(B)=2 | NB-COIN · NHBSA |
| Edge | Which item tends to immediately follow i? | D→B | COIN · EHBSA |
| Precedence | Does i tend to appear before j? | A ≺ C | Order-based models |
| Relative displacement | How far and in which direction is j from i? | Δ(A,C)=+4 | ROSE · SR-ROSE · SH-ROSE |
Why signed distance? The sign preserves before/after; the magnitude preserves spacing. Adjacency is the special case |Δ|=1, while precedence keeps only the sign.
Design choice
Representation is a hypothesis
Choose edge
When local succession is the building block, as in routes or transition-dependent costs.
Choose relative order
When both precedence and separation matter, but an exact absolute position may move between good solutions.