How functional dependencies can help full and partial materialization of skycubes

How functional dependencies can help full and partial materialization of skycubes

• How functional dependencies can help full and partial materialization of skycubes

Discard records with low quality is one dimension of data cleaning

• Discard records with low quality is one dimension of data cleaning

• Compare tuples wrt their respective quality parameters

• Best tuples = those with best tradeoff wrt quality parameters

Intuitive idea:

• Intuitive idea:

• For every A, find the maximal X st X  A

• Every x  X’s is potentially closed

• The intersection of these sets of x’s are the closed subspaces

Let X be a subspace.

• Let X be a subspace.

• Let Closed={Y | Y is closed}

• Then, X+ = smallest Y Closed s.t X  Y

Definition: X ↬ Y iff t[X]=t’[X]  t[Y] and t’[Y] incomparable

• Definition: X ↬ Y iff t[X]=t’[X]  t[Y] and t’[Y] incomparable

• Theorem: Sky(X) satisfies X ↬ Y  Sky(X)  Sky(XY)

• Property: XY  X ↬ Y

Expression = Sky(AB & CD)

• Expression = Sky(AB & CD)

• First computes Sky(AB)

• If t[AB] = t’[AB] and t Sky(AB), then t and t’ are compared wrt C and D

Let  = X1 & … & Xi & … & Xm

• Let  = X1 & … & Xi & … & Xm

• If X1…Xi-1  X and X  Xi then

•  ’ = X1& … & Xi\X & … & Xm

• AB  C  Sky(AB & CD)  Sky(AB & D)

Functional dependencies are helpful for both full and partial skycube materialization

• Functional dependencies are helpful for both full and partial skycube materialization

• Incomparability dependencies characterize skyline inclusions

• Semantic optimization of prioritized skylines with FDs

Is it possible to come up with a Chase like procedure for priotirized skylines semantic optimization?

• Is it possible to come up with a Chase like procedure for priotirized skylines semantic optimization?

• What about Order dependencies ?

• Incremental maintenance

• Approximate skylines and approximate FDs

• t[A] is preferred to s[A] iff s[A] – t[A] > 
• X  Y iff t, s : t[X] ~ s[X]  t[Y] ~ s[Y]

Thanks

• Thanks

• Questions