Databases Reference
In-Depth Information
-
α
∩
st
N
: Spatiotemporal extent of
α
overlaps with that of
N
.
-
α
⊗
st
N
: Spatiotemporal extent of
α
is disjoint with that of
N
•
Profile Bounding Vector Relationship
-
α
→
⊃
p
N
→
:
α
→
encloses
N
→
if for each non-zero profile attribute
vector
4
of
α
→
and
N
→
, bitwise 'OR' operation of
α
→
and
N
→
results
in
α
→
.
α
→
∩
p
N
→
:
α
→
overlaps with
N
→
if for each non-zero profile attribute
of
α
→
and
N
→
, their bitwise 'AND' operation results in a non-zero
profile attribute vector.
-
α
→
⊗
p
N
→
:
α
→
is disjoint with
N
→
if for each non-zero profile attribute
of
α
→
and
N
→
, their bitwise 'XOR' operation results in all “1”s in the
resultant vector.
-
The spatiotemporal relationships are handled similar to that in earlier
sections. Profile bounding vector relationships between an authorization and
a node are handled as follows. First, in case of enclosing relationship, observe
that for every bit value of '0' of
α
→
, the corresponding bit value of
N
→
must be '0' because there must not exist any profile attribute value that
only
N
→
includes but
α
→
does not. Therefore, bitwise 'OR' operation would
generate the same value with
α
→
. Also, in case of overlapping relationship,
one need to see if there exists any common profile attribute value between
α
and
N
→
. Therefore, if bitwise 'AND' operation results in a non-zero profile
vector, we know that there exists common value set. Finally, in case of disjoint
relationship, it is obvious that
α
and
N
→
should not share any profile attribute
value that is common to each other. The bitwise 'XOR' operation is used for
checking this condition, and the result of 'XOR' must include all '1's in the
resultant
N
→
.
α
→
N
→
AND OR XOR Relationship
110 011
010 111 101
α
→
∩
p
N
→
010 110 100
α
→
∩
p
N
→
,
α
→
⊃
p
N
→
110 010
000 111 111
α
→
⊗
p
N
→
Table 3.
Bitwise Operation Results
110 001
The authorizations overlaying procedure traverses the S
STP
-tree from the
root node to leaf level by recursively comparing both the spatiotemporal ex-
tents and
PV
B
s of the overlaying authorization and each node in the traversal
path. The following possible cases are encountered.
•
Case 1:
If (
α
encloses
N
)
∧
(
α
→
encloses
N
→
) is true, traversal is
stopped and
α
is overlaid on
N
.
4
A non-zero profile attribute vector refers to a binary vector that includes the
value “1” in at least one bit
