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who satisfy the query will be moving inside Essex County during the time
interval. The evaluation proceeds as follows: In this case, for each customer
and for each spatiotemporal window that the customer passes through, a set
of search keys are created. Two spatiotemporal windows are possible: (Essex
County, During Working Hours) and (Essex County, After Working Hours).
Thus, the search key includes object
, the requester ID of Hilton, and a
spatiotemporal window for each customer. The search operation is done in the
order of the auth-object, the auth-subject, the location, and the time interval
hierarchies since this same order is used in the authorization specification.
The approach using the ASM-Trie is not capable of providing unified index
for authorizations and mobile objects. Moreover it considers the case where the
auth-subjects are only static but cannot handle the cases when both subjects
and objects are moving.
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5 Unified Index for Authorizations and Moving Objects
The following two approaches have been proposed in the literature of unified
index scheme for authorizations and moving objects.
S
TPR-Tree:
Unified index for present and anticipated future locations of
moving objects and authorizations.
•
S
PPF
-Tree:
Unified index for past, present, and anticipated future loca-
tions of moving objects and authorizations.
•
Both of unified index schemes consider the cases of mobile requesters upon
static resources and static requesters upon mobile resources, but not mobile
requesters upon mobile resources.
s
TPR-Tree
5.1
S
TPR-tree is constructed by appropriately overlaying authorization on the
TPR-tree [11], which in turn is a variant of the R-tree. Because the locations of
moving objects are constantly updated, the main challenge for moving object
database is to minimize the updating cost. For this purpose, in the TPR-tree,
the moving object is represented as its initial location and its velocity vector;
thus, a moving object is updated only if it deviates more than the specified
tolerance level. This will reduce the necessity for frequent updating. Moreover,
since the velocity of moving objects is also maintained, it can estimate their
anticipated future locations.
Unlike the traditional
Minimum Bounding Rectangle
(MBR) in R-trees
[8], a
Time-Parameterized bounding Rectangle
(TPR) is used to index velocity
vectors as well as location information. However, given a moving object, it is
unrealistic to assume that its velocity remains constant. The predicted future
location of a object specified as a linear function of time becomes less and
less accurate as time elapses [11]. To address this issue, the TPR-tree defines
