Database Reference
In-Depth Information
Table 3. Skyline for each subset of multidimensional criteria
Subset
Skyline
{EDBT, ICDE, VLDB, SIGMOD}
{5932; 8846; 19660; 20259; 23870}
{ICDE, VLDB, SIGMOD}
{5932; 8846; 19660; 20259; 23870}
{EDBT, VLDB, SIGMOD}
{5932; 8846; 20259; 23870}
{EDBT, ICDE, SIGMOD}
{5932; 8846; 19660; 23870}
{EDBT, ICDE, VLDB}
{5932; 8846; 19660; 23870}
{VLDB, SIGMOD}
{8846; 20259; 23870}
{ICDE, SIGMOD}
{5932; 19660; 23870}
{ICDE, VLDB}
{5932; 8846; 19660; 23870}
{EDBT, SIGMOD}
{5932; 8846; 23870}
{EDBT, VLDB}
{8846}
{EDBT, ICDE,}
{8846; 19660}
{EDBT}
{8846}
{ICDE}
{19660}
{VLDB}
{8846}
{SIGMOD}
{23870}
natural ordering over
p
attributes. We define the Skyline SKY
S
on a space
S
according to a multicriteria
function
m
as follows:
SKY
S
= {o
i
| o
i
∧
DO
: (¬
∧
o
j
| o
j
∧
DO
: s
1
(o
j
)≥s
1
(o
i
)
∧
…
∧
s
q
(o
j
)≥s
q
(o
i
)
∧
(
∧
x | 1 ≤ x ≤ q: s
x
(o
j
)>s
x
(o
i
)))}
The conditions to be satisfied by the answers of a Top-k Skyline query with respect to the functions
m
and
f
, are described as follows:
ξ
<f,m,k>
= { o
i
| o
i
∧
SKY
S
∧
(¬
∧
k-|SKYs|
o
j
| o
j
∧
SKY
S
: f(o
j
) ≥ f(o
i
))}
Where,
∧
t
means that exists at most
t
elements in the set. Additionally, the Skyline Frequency may
be used as a score function to rank the Skyline:
ξ
<sf,m,k>
= { o
i
| o
i
∧
SKY
S
∧
(¬
∧
k-|SKYs|
o
j
| o
j
∧
SKY
S
: sf(o
j
) ≥ sf(o
i
))}
Where the Skyline Frequency of a object
o
∧
SKY
S
, denoted by
sf(o)
, is the number of subspaces
S
'
of
S
in which
o
is a Skyline object, this is:
sf(o) = (∑ S' | S'
∧
S
∧
o
∧
SKY
S'
: 1)
The Skycube or lattice is the set of the all Skylines for any subspace S' of S defined as:
SkyCube = {
∧
SKY
S'
| S'
∧
S}
