NestedRelations: 1

Nested Relations

• Flat schemas often have replicated data values in their relations.

• Nested schemas allow us to collapse some of these replicated data values.

NrBeds RoomNr (NrBeds ( RoomNr )* )* 2 1 2 1 2 2 2 2 3 3 1 4 1 4 1 5 5

NestedRelations: 2

Redundancy in Nested Schemes• The redundancy definition is the same as for flat relations.• If a hidden value can be uniquely determined or if a value change

causes a constraint violation, the value is redundant.

RoomNr ViewNrBeds RoomNr ViewNrBeds

(NrBeds (RoomNr (View)* )* )* 2 1 Sea Forest City

2 Sea Forest

3 City

(View (RoomNr NrBeds)* )* Sea 1 2

2 2

Forest 1 2 2 2

City 1 2 3 2

NestedRelations: 3

NNF: Redundancy Free Nested Schemas

Input: a canonical, acyclic, binary hypergraph H.

Output: a set of nested schemas with no potential redundancy.

Repeat Mark an unmarked node in H as the first attribute in a new nested schema. While an unmarked edge is incident on a marked node A: Mark the edge. If A B: Add B with A; Mark B. If A B: Add B with A; Mark B if all B’s incident edges are marked. If A B: Nest B under A; Mark B. Else (A — B): Nest B under A; Mark B if all B’s incident edges are marked.Until all nodes have been marked

NestedRelations: 4

Nested Schema Generation Example

GuestNr GuestNameRoomNr

ViewCostRoomName

NrBeds GuestNr GuestNameRoomNr

ViewCostRoomName

NrBeds

1. (NrBeds, (RoomNr, RoomName, Cost, (View)*, (GuestNr, GuestName)* )* )*

2. (RoomNr, RoomName, Cost, NrBeds, (View)*, (GuestNr, GuestName)* )*

3. (GuestNr, GuestName, RoomNr)* (RoomNr, RoomName, Cost, NrBeds (View)* )*

NestedRelations: 5

Redundancy Prevention

xa 1

yb 2

z

(A ( B C )* )* a x 1

y 1 2

b y 1 2

z 2This replication ...

… causes thisredundancy.

NestedRelations: 6

Generalizationfor N-ary Relationship Sets

C

B

A D

C

B

A D

• “Composite nodes” can be treated as a single node.– (B C (A)* (D)* )*– (D (B C)* )*; (A B C)*

• Or, n-ary edges (n3) can be converted to an object set and n binary relationship sets.

• NNF, basically:– Schemes should be constructed along hypergraph paths.– Schemes should not violate the natural 1-many hierarchical structure.