Location-based Spatial Queries

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Location-based Spatial Queries

• 
  AGM SIGMOD 2003
• Jun Zhang, Manli Zhu, Dimitris Papadias, Yufei
  Tao, Dik Lun Lee
• Department of Computer Science
• Hong Kong University of Science and Technology
• and
• Carnegie Mellon University
• Presented By
• Sreepraveen Veeramachaneni

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary
• References

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Introduction

• The paper proposes an approach that enables
  mobile clients to determine the validity of
  previous queries based on their current location.
• Two types are spatial queries are discussed
• 1.Window Queries
• 2.Nearest Neighbor Queries

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Techniques In use

• Spatial databases have been extensively studied
  during the last two decades and several spatial
  access methods have been proposed.
• The most popular one is R-tree and its variations
  like R -tree.
• R-trees can be viewed as multi-dimensional
  extensions of B-trees.

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R-treeAssuming capacity of 3 entries per node.
Points that are close in space are clustered in
the same leaf node represented as a MBR. Nodes
are then recursively grouped together following
the same principle until the top level, which
consists of a single root
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R tree Contd.

• This technique is used to answer window queries
• Another important type of spatial information
  processing is nearest neighbor query, which
  retrieves the data point that is closest to a
  query point

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Branch and Bound Algorithm

• Roussopoulos et al., proposed a branch and bound
  algorithm that searches the R-tree in a depth
  first manner.
• Starting from root, all entries are sorted
  according to their minimum distance from the
  query point, and the entry with the smallest
  value is visited first.
• The process is repeated recursively until the
  leaf level where the first potential nearest
  neighbor is found.
• During backtracking to upper levels, the
  algorithm only visits entries whose mindist is
  smaller than the distance of the nearest neighbor
  already found.

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary

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Traditional Scenario

• The traditional scenario in spatial databases
• assumes that
• Queries are static and
• Each query returns a single output and terminates.

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Where Is Your Nearest Restaurant?

• Traditional nearest neighbor search in spatial
  databases considers static query points.

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What if You Move?

• Getting only the nearest neighbor is inadequate
  When will it expire?

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• The conventional approach to attain up-to-date
  information is to pose a new query to the server
  after a position update, which could lead to high
  network overhead and extra processing effort.
• And due to high mobility of the user, the result
  may be invalidated immediately as the users
  position changes

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary

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First spatial query processing Technique for
Mobile computing Zheng, Lee SSTD 2001

• The first technique was to pre-compute and store
  in an R-tree the Voronoi diagram of the dataset.
• Voronoi Diagram The Voronoi diagram of a
  collection of geometric objects is a partition of
  space into cells, each of which consists of the
  points closer to one particular object than to
  any others

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• When a nearest neighbor query arrives at the
  server, the Voronoi diagram is used to
  efficiently compute the nearest neighbor

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• In addition to result, the server sends back to
  the client the client the validity time T of the
  result, which is a conservative approximation
  assuming that the querys speed is below a
  maximum value.
• Problem Difficult to estimate the value of Query
  speed. A high value will result in very short T
  and a low value will result in false misses
• The method only deals with single nearest
  neighbor queries and retrieval of K neighbors
  would require order-K Voronoi diagrams , which
  are complicated and incur large space overhead.

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K- Nearest neighbor query Song, Roussopoulos,
SSTD 2001

• Song and Roussopoulos proposed a technique that
  does not assume Voronoi diagrams and can be used
  for any number of neighbors.
• When a k nearest neighbor query q arrives, the
  server computes and returns to the client a
  number m gt k of neighbors.

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Implementation

• Let dist (k) and dist (m) be the distances of the
  kth and mth nearest neighbor from the query point
  q.
• If the client re-issues the query at a new
  location q, the new k nearest neighbors will be
  among the m objects of the first query, provided
  that
• 2.dist(q,q) dist(m) dist(k)

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Example

• The figure shows an example for a 2-nearest
  neighbor query at location q, where the server
  returns four results o, a, b and c ( the nearest
  neighbors are o and a)
• When the client moves to the location q, the two
  NN are o and b.
• If 2.dist(q, q) dist(4) dist(2), the client
  can determine this by computing new distances
  (wrt to q) of the four objects, with out having
  to issue a new query to the server

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Problems

• An obvious problem of this approach lies in
  obtaining a proper value of m
• A high value will increase the network overhead
  and the storage requirements at the client, while
  a low value may be useless( if it does not reduce
  the number of queries)
• m depends on factors like data distribution and
  query frequency which are difficult to estimate

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Time Parameterized Nearest Neighbor (TP NN) Tao
and Papadias, SIGMOD02

• Given a query moving with steady velocity, return
  all nearest neighbor results ( up to a future
  timestamp), i.e., the output is a set of tuples
  ltRi, Tigt, where Ri is the set of nearest
  neighbors during future interval Ti
• For this situation, the concept of time
  parameterized queries can be applied for both
  window queries and nearest neighbor queries.
• When a server receives a request from a client ,
  it executes a TP query and returns ltR,T,Cgt, where
  R is the set of objects satisfying the
  corresponding spatial query (current result), T
  is the validity time of R, and C is the result
  change at T
• From the set of objects in R, and the set of
  objects in C that will cause the changes , the
  client can incrementally compute the next result

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TP window Query

• Consider, that a client moving east with speed
  one issues a window query.
• The server returns ltb, 1, -bgt meaning that
  object b currently intersects the query window,
  but after 1 time unit it will stop doing so and
  therefore, b should be removed from the result.

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Influence of a Object

• The result of a spatial query changes in future
  because some objects influence its correctness.
• If an object (e.g., b) satisfies the query at the
  current time, it may influence the result when it
  no longer satisfies it in the future (at time 1).
• An object not currently in the result (e.g., d)
  may influence the query when it becomes part of
  the result (at time 2).
• Some objects such as a and c, may never change
  the result, so their influence time is set to 8

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Time Parameterized Nearest Neighbor (TP NN)Tao
and Papadias, SIGMOD02

• Returns
• The nearest neighbor R of the current query
  location
• The expiry time T of R (given the querys
  movement)
• The change C of the result at T

Result Ri, T2, Cj
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Problem with the techniques discussed so far

• All the techniques we discussed for mobile
  computing presuppose that future locations of
  clients can be calculated using their current
  movements (i.e., the velocity of client is known
  and constant during the lifespan of the query)
• But in many applications query velocities are
  continuously updated as the users change their
  speed or direction of movement
• Motivated by this, the authors introduce a
  technique where, instead of time, the validity of
  the result is determined by the users location in
  space.

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary

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Location-Based Nearest Neighbors

• Assumptions
• We assume that there exists a spatial index
  (e.g., R-trees) for data objects, but no
  specialized structures (e.g., Voronoi diagrams)
  for nearest neighbor search.

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Getting You Covered by the Nearest Restaurant

• Some users (say, a tourist walking causally)
  cannot specify their heading directions clearly.

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Validity Region of the Result

• In addition to the nearest restaurant, we also
  return the validity region of this restaurant.
• Another query is issued to retrieve the new
  nearest restaurant, only if the user moves out of
  this region.

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Influence Points

• Points that determine the influence region.

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Influence Points

• Keeping the influence points avoids the
  in-polygon check.
• The user only needs to check if her/his location
  is closer to any yellow point than a.

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Validity Region A Closer Look

• The validity region of q is the Voronoi Cell (VC)
  of o.

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Pre-Compute the Voronoi Diagram?

• Bad idea!
• To answer kNN of a specific value k, a k-order
  Voronoi Diagram is necessary.
• If we want to answer NN, 2NN, , 20NN, then 20
  sets of Voronoi Diagrams are necessary.
• Huge space!
• Poor support for data update.
• Our solution Compute the cell on the fly.
• Use a single R-tree
• Support all values of k

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Relationship with Time Parameterized NN

• If q moves towards l, then its nearest restaurant
  will change to point a at position q.
• The corresponding TP query q returns (i) o,
  (ii), a, and (iii) q.

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Algorithm

• Step 1 Find the current NN
• Step 2 Use TP NN queries to tighten the
  validity region progressively

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Algorithm

• Step 2 Use TP NN queries to tighten the
  validity region progressively

• The algorithm issues totally 2Sinf TP NN queries,
  where Sinf is the number of influence points.
• This algorithm generalizes to computing k-order
  Voronoi Cells for arbitrary values of k (see the
  paper for details).

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Extensions to k NN queries

• The above method can be easily applied to k
  nearest neighbor queries, where the validity
  region is the maximal area around the query,
  where each point has the same set of k nearest
  neighbors.

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary
• References

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Location-based Window Queries Find All Close
Restaurants

• Some users would consider more restaurants in
  their vicinity.
• The validity region here is such that, as long as
  the user stays in this region, the query result
  does not change.

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Location-based Window Queries

• The focus f of the window query q is the centroid
  of the query window
• The validity region V (q) of a query q is the
  maximal area around the query focus (i.e., f ? V
  (q)) where the query result R (q) does not change
• The points that satisfy q are called inner
  objects, and those outside the query window outer
  objects

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Location-based Window Queries

• The Minkowski region of each point (e.g., a) is a
  rectangle (ra) identical to the query window
  whose centroid lies on the corresponding point
  (a)
• If query focus moves inside ra, the query result
  always contains object a.
• The intersection of the inner Minkowski regions
  corresponds to inner validity region.

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The Validity Region of Window Queries

• If the user location is at the boundary of the
  validity region, the corresponding query windows
  boundary will cross some data point.

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The Validity Region of Window Queries

• If the user location is at the boundary of the
  validity region, the corresponding query windows
  boundary will cross some data point.

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The Validity Region of Window Queries

• If the user location is at the boundary of the
  validity region, the corresponding query windows
  boundary will cross some data point.

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The Validity Region of Window Queries

• If the user location is at the boundary of the
  validity region, the corresponding query windows
  boundary will cross some data point.

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The Influence Points

• In addition to the query result a,b,c, the user
  is also aware of 2 inner influence points a,b
  and 2 outer influence points d,e.
• The original result is invalidated if the query
  window
• Does not cover any inner influence point.
• Covers any outer influence point
• The user does not need to store the actual
  boundary of the validity region).

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Retrieving the Influence Points

• First get the query result a,b,c (a traditional
  window query).
• Then the influence points.
• Using Time Parameterized Window Queries (see
  paper).

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Outline

• Introduction
• General techniques in spatial query Processing
• Motivation
• Background
• Location-based nearest neighbor search
• Location-based window queries
• Experiments
• Summary
• References

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Experiments

• Datasets
• GR (23K, data space 800km?800km),
• NA (569K, data space 7000km?7000km)
• Disk page size set to 4k bytes
• Index R-tree
• Queries
• LB kNN parameter k
• LB WQ parameter query length
• Each workload consists of 200 queries with the
  same parameters distributed uniformly in the data
  space.

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Experiments

• The area of validity region drops linearly with
  cardinality since the number voronoi cells
  increases ( while the area of data space remains
  constant).
• Under all settings the average number of edges
  in a voronoi cell is 6 for uniform datasets which
  is equal to number of influence objects.

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Experiment 1 Number of Influence Points for LB
kNN

• The number of influence objects decreases to 4
  for kgt10. this is because for kgt1, an influence
  object may contribute more than one edge (since
  it can form perpendicular bisector with any of
  the k nearest neighbors of the query), while the
  total number of edges remains around 6.

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Experiment 2 Query cost for LB kNN

• The above figure shows the number of node
  accesses as a function of cardinality for k 1
• The number of nodes accesses for TPNN queries is
  about 12 times that of the regular nearest
  neighbor query because, on average we need 6 TPNN
  queries to retrieve the influence objects and
  another 6 queries to confirm the vertices of the
  validity region.

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Experiment 2 Query cost for LB kNN with a buffer

• As we can see, using an LRU buffer equal to 10
  of the R-tree size the actual cost of TPNN
  queries reduces significantly, since all the
  queries access similar parts of the data space.
• Thus, given a relatively small buffer, the
  overhead imposed by location-based NN queries is
  not significant

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Experiment 3 Number of Influence Points for LB WQ
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Experiment 4 Query cost for LB WQ
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Conclusion

• Location-based queries retrieve the validity
  regions for the query results.
• We considered kNN and window queries.
• Future work
• Apply the concept of validity region to other
  types of queries (e.g., range queries).
• Study the incremental computation of the query
  result (i.e., what happens after the user exits
  the validity region?)

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References

1. Song, Z., Roussopoulos, N. K-Nearest Neighbor
   Search for Moving Query Point. SSTD 2001
2. Tao, Y., Papadias, D. Time Parameterized Queries
   in Spatio-Temporal Databases. SIGMOD 2002
3. Zheng, B., Lee, D. Semantic Caching in Location
   Dependant Query Processing. SSTD 2001
4. Roussopoulos, N., Kelly, S., Vincent, F. Nearest
   Neighbor Queries. SIGMOD 1995