Indexing and Range Queries in SpatioTemporal Databases

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

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Outline

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

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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.

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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.

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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

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R-tree Insertion
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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

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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.

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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.

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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
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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
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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.
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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.

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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.

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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).

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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).

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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.

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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.

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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.

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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

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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.

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TPR-tree
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TPR-tree
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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

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QA
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Thanks!