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Indexing and Range Queries in SpatioTemporal Databases

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21. Experiments: Settings (query and tree) Dataset. 50,000 sampled objects' MBRs are taken from a real spatial dataset NJ [Tiger] ... – PowerPoint PPT presentation

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Title: Indexing and Range Queries in SpatioTemporal Databases


1
Indexing and Range Queries in Spatio-Temporal
Databases
Danzhou Liu, Wei Cui, Yun Fan School of
Computer Science University of Central Florida

2
Outline
  • Introduction
  • The R-tree
  • The TPR-tree
  • The TPR-tree
  • Experiments
  • Conclusions

3
Introduction
  • Spatio-temporal databases
  • record moving objects geographical locations
    (sometimes also shapes) at various timestamps.
  • support queries that explore their historical and
    future (predictive) behaviors. Applications.
  • applications flight control systems, weather
    forecast and mobile computing
  • The database stores the motion functions of
    moving objects.
  • For each object o, its motion function gives its
    location o(t) at any future time t.
  • A predictive window query
  • specifies a query region qR and a future time
    interval qT
  • retrieves the set of all objects that will fall
    in qR during qT.
  • our goal index moving objects so that a
    predictive window query can be answered with as
    few disk I/Os as possible.
  • Examples
  • Find all airplanes that will be over Florida in
    the next 10 minutes.
  • Report all vessels that will enter the United
    States in the next hour.

4
Motion Function
  • We consider linear motion.
  • For each object, the database stores
  • Its minimum bounding rectangle (MBR) at the
    reference time 0
  • Its current velocity bounding rectangle (VBR)
  • Examples MBR(a)2,4,3,4, VBR(a)1,1,1,1
    MBR(c)8,9,3,4, VBR(c)-2,0,0,2
  • An update is necessary only when an objects VBR
    changes.

5
R-tree
  • The R-tree aims at minimizing
  • the area
  • The perimeter of each MBR
  • The overlap between two MBRs (e.g., N1, N2) in
    the same node
  • The distance between the centroid of an MBR and
    that of the node containing it

6
R-tree Insertion
7
The Time Parameterized R-Tree (TPR-Tree)
  • Extends the R-tree by introducing the velocity
    bounding rectangle (VBR) in all entries.
  • Queries are compared with conservative MBRs of
    non-leaf entries. N1v-2,1,-2,1 and
    N2v-2,0,-1,2

8
TPR-Tree
  • Our goal
  • index moving objects so that a predictive window
    query can be answered with as few disk I/Os as
    possible.
  • A mathematical model that estimates the cost of
    answering a predictive window query using
    TPR-like structures.
  • Number of node accesses.
  • Application of the model to derive the optimal
    performance.
  • The TPR-tree is much worse than the optimal
    structure.
  • Exam the algorithms of the TPR-tree, identify
    their deficiencies, and propose new ones.
  • The TPR-tree.

9
TPR deficiency 1 Choosing sub-tree to insert
  • To insert an entry, the TPR-tree picks the
    sub-tree incurring the minimum penalty (smallest
    MBR/VBR enlargement).
  • May result in inserting an entry into a bad
    sub-tree this problem is increasingly serious as
    time evolves.

10
TPR solution Choose path
  • Aims at finding the best insertion path globally,
    namely, among all possible paths.
  • Observation We can find this path by accessing
    only a few more nodes (than the TPR-tree
    algorithm).

Maintain a heap (g),0, (h),0, (i),20
the path expanded so far
the accumulated penalty so far
11
TPR solution Choose path
  • Aims at finding the best insertion path globally,
    namely, among all possible paths.
  • Observation We can find this path by accessing
    only a few more nodes (than the TPR-tree
    algorithm).

Visit node g (h),0, (a,g),3, (i),20,
(b,g),32
complete paths already although nodes a and b are
not visited
12
TPR solution Choose path
  • Aims at finding the best insertion path globally,
    namely, among all possible paths.
  • Observation We can find this path by accessing
    only a few more nodes (than the TPR-tree
    algorithm).

Visit node h (a,g),3, (d,h),9, (c,h),17,
(i),20, (b,g),32
The algorithm stops now.
13
TPR deficiency 2 Which entries to re-insert
  • When a node overflows, some of its entries are
    re-inserted to defer node split (the ones that
    diverge most from the node centroid).
  • The entries chosen by the TPR-tree are very
    likely to be re-inserted back to the same node,
    so that a node split is still necessary.

14
TPR solution Pick worst
  • Aims at selecting entries that can most
    effectively shrink the MBR or VBR of the node
    for re-insertion.
  • The first step picks an appropriate dimension
    (either spatial or velocity) based purely on
    estimation using our cost model (see the paper
    for details).
  • The second step performs sorting on this
    dimension and decides the entries to be removed .
  • Example If the axis chosen in the first step is
    the x-axis, then the sorting list is b,d,a,c.
    Either b or c is removed.

15
TPR deficiency 3 Tightening MBR in deletion
  • Entry deletion requires first finding the entry,
    which accesses many nodes of the tree. The
    TPR-tree uses this fact to tighten the MBR of
    non-leaf entries.
  • Assume nodes h and i are accessed before e is
    found then the TPR-tree will tighten the MBR of
    i only (enclosing g and f).

16
TPR deficiency 3 Tightening MBR in deletion
  • Entry deletion requires first finding the entry,
    which accesses many nodes of the tree. The
    TPR-tree uses this fact to tighten the MBR of
    non-leaf entries.
  • Assume nodes h and i are accessed before e is
    found then the TPR-tree will tighten the MBR of
    i only (enclosing g and f).

17
TPR solution Active tightening
  • Tightening more entries for free.
  • Assume nodes h and i are accessed before e is
    found then the TPR-tree will tighten the MBR of
    both h and i.

18
TPR solution Active tightening
  • Tightening more entries for free.
  • Assume nodes h and i are accessed before e is
    found then the TPR-tree will tighten the MBR of
    both h and i.

19
TPR solution Active tightening (Cont.)
  • Another example Assume the shaded nodes are
    accessed to find e.
  • The active tightening can tighten the MBR of n5,
    n6, n3, and n4.
  • But not n1 and n2.

20
Challenge of Migration
  • 3 Operating Systems
  • Microsoft Windows
  • Sun Solaris
  • Redhat Fedora Core 1
  • 2 Compilers CL, GCC (2.9.5, 3.3.2)
  • Difference of Code Conversion
  • How close the compilers to the standard?
  • Compatibility of Library

21
Experiments Settings (query and tree)
  • Dataset
  • 50,000 sampled objects MBRs are taken from a
    real spatial dataset NJ Tiger
  • each object is associated with a VBR such that on
    each dimension
  • The velocity extent is zero (i.e., the object
    does not changespatial extents during its
    movement)
  • the velocity value distribution is randomed in
    range 0,8
  • the velocity can be positive or negative with
    equal probability.
  • We compare TPR- with TPR-trees.
  • Disk page size1k bytes (node capacity27 for
    both trees).
  • For each object update, perform a deletion
    followed by an insertion on each tree.
  • Each predictive query is a moving rectangle, and
    has these parameters
  • qRlen The length of the querys MBR
  • qVlen The length of the querys VBR
  • qTlen The number of timestamps covered.

22
TPR-tree
23
TPR-tree
24
Conclusions
  • The TPR-tree combines the idea of conservative
    MBR directly with the tree construction
    algorithms of R-trees.
  • The TPR-tree improves it by designing algorithms
    that take into account the special features for
    moving objects.
  • Cost model for performance analysis
  • The optimal performance of a hypothetically best
    structure
  • Reduce disk I/Os for predictive queries

25
QA
26
Thanks!
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