kNR-tree:%20A%20novel%20R-tree-based%20index%20for%20facilitating%20Spatial%20Window%20Queries%20on%20any%20k%20relations%20among%20N%20spatial%20relations%20in%20Mobile%20environments

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kNR-tree A novel R-tree-based index for
facilitating Spatial Window Queries on any
krelations among N spatial relations in Mobile
environments

• ANIRBAN MONDAL
• IIS,
• University of Tokyo.

ANTHONY K. H. TUNG SOC, National University of
Singapore
MASARU KITSUREGAWA IIS, University of Tokyo.

• Contact E-mail anirban_at_tkl.iis.u-tokyo.ac.jp

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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INTRODUCTION

• Increasing popularity of mobile applications
• Prevalence of spatial data and its applications

Efficient processing of spatial queries in mobile
environments
This work focusses on the processing of spatial
select queries on any k relations among N spatial
relations in mobile environments ? kNW queries
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Motivation for kNW queries

• A single client may be interested in objects from
  a number of different relations
• Different clients may be interested in different
  numbers as well as different kinds of relations.
• Mobile environments typically have multiple
  relations and user population demographics may
  vary considerably.

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Examples of kNW queries

• Find all bookshops, restaurants and car-parks
  which I will encounter nearby me during my next
  10 minutes of travelling.
• Find all bus stations and shopping centres which
  I will encounter nearby me during my next 15
  minutes of travelling.

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Examples of kNW queries

• Find all bookshops, restaurants and car-parks
  which I will encounter nearby me during my next
  10 minutes of travelling.
• Find all bus stations and shopping centres which
  I will encounter nearby me during my next 15
  minutes of travelling.

kNW queries are beneficial in the real world.
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MAIN CONTRIBUTIONS

• Proposal of the kNR-tree, a single integrated
  novel R-tree-based structure for indexing objects
  from N different spatial relations.
• kNR-tree facilitates kNW queries.
• Processing of kNW queries in mobile environments
• Differences from existing works
• The window of the query is speculative (not known
  in advance)
• the processing done by some of the base stations
  may not contribute to the final results.
• We examine issues concerning objects from N
  different spatial relations.

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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PROBLEM FORMULATION

• Given a set of base stations, each of which
  stores and manages the data (from N spatial
  relations) of mutually disjoint spatial regions
  and a set of mobile clients, the mobile client
  wishes to find the results of spatial window
  queries (on any k of the N relations) nearby
  himself within the duration of the next T time
  units.

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THE CONTEXT

• Each object is a point in space represented by
  its centroid.
• Each object has a corresponding descriptor
  bitmap.
• The descriptor bitmap for each object is exactly
  the same in terms of the entry positions of
  relation.
• Tick entry positions as 1 if object has the
  relation, otherwise mark as 0.
• Objects are static, but the clients who issue
  queries to the objects are mobile.
• Alternative perspective of this problem Indexing
  only one spatial relation with the type of the
  object as
• a scalar attribute of the space.

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ILLUSTRATIVE EXAMPLE OF OBJECT BITMAPS
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CLIENT QUERIES

• Client queries are of the form (queryID,
  clientID, PIssue, SpeedMax, Qbitmap, Delta, Tau)
• queryID is the unique query identifier
• clientID is the unique client identifier
• PIssue is the point of issue of the query
• SpeedMax specifies clients maximum speed.
• Qbitmap is the query bitmap (an array of N bits)
• Structure is exactly same in terms of entry
  positions of relations as object bitmap.
• Delta quantifies the distance from clients
  current location which M considers to be nearby
  himself.
• Tau indicates the duration of time (after issuing
  the query) during which the client would wish to
  receive the query results.

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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WINDOW QUERY PROCESSING IN MOBILE ENVIRONMENTS

• We define Qcircle as a circle drawn with PIssue
  as centre and (Tau SpeedMax Delta) as radius.
• MBR of Qcircle is called QMBR.
• Client cannot be traveling at his maximum speed
  in all directions at once
• QMBR is a speculative and conservative estimate
  of the query window
• QMBR may intersect with the domains of multiple
  base stations

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Case 1

• QMBR falls completely within one base station Bs
  domain
• B processes QMBR on its own and sends results to
  client.

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Case 2

• QMBR intersects with the domain of at least one
  base station other than B
• B determines the set R of base stations with
  whose domains QMBR intersects.
• For each member r of R, B determines the
  intersecting rectangular part between QMBR and
  rs domain and sends the intersecting rectangular
  part to each r.
• We refer to such intersecting rectangular parts
  as subQMBRs.
• After processing its respective subQMBR, each r
  sends a COMPLETE message to indicate that it has
  completed processing its subQMBR.

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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The kNR-tree

• kNR-tree is a single integrated Rtree-based
  structure for indexing objects from N spatial
  relations.
• Non-leaf nodes of the kNR-tree contain entries of
  the form (ptr, mbr, Nbitmap)
• ptr is a pointer to a child node in the kNR-tree
• mbr is the MBR that covers all the MBRs in the
  child node.
• Nbitmap consists of array of N entry bits, one
  for each spatial relation.
• Leaf nodes of the kNR-tree contain entries of the
  form (oid, loc, Nbitmap)
• oid is a pointer to an object in the database
• loc is the location of the object.

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Illustrative example of kNR-tree
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Window query processing algorithm for kNR-tree
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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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PERFORMANCE STUDY

• Real dataset Greece Roads used for our
  experiments
• The Greece Roads dataset contains 23268
  rectangles.
• We computed the centroid of these rectangles to
  get 23268 points
• Enlarging this dataset of points by translating
  and mapping the data.
• Each of the base stations had more than 200000
  points (objects)
• Each point associated with at least one spatial
  relation
• We used 16 base stations
• kNR-tree used for indexing the points at each
  base station
• We define the size of a query QSIZE as the
  percentage of a base stations domain that a
  query covers.
• Example QSIZE 20 implies that the query
  covers 20 of the area associated with the base
  stations domain.
• We used a fanout of 64 for the kNR-tree

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Effect of variations in QSIZE
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Effect of variations in k
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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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RELATED WORK

• Traditional R-tree-based indexes are not adequate
  for indexing mobile objects
• Frequent updates ? large number of node-splits
  and/or node-merges.
• R-tree-based structures for mobile context
• Time-parameterized R-tree (TPR-tree)
• Spatio-Temporal R-tree (STR-tree)
• Trajectory-Bundle tree (TB-tree)
• Lazy Update R-tree (LUR-tree)
• Multiversion 3D R-tree(MV3R-tree)

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PRESENTATION OUTLINE

• INTRODUCTION
• PROBLEM FORMULATION
• QUERY PROCESSING
• The kNR-tree index
• PERFORMANCE STUDY
• RELATED WORK
• CONCLUSION AND FUTURE WORK

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CONCLUSION AND FUTURE WORK

• Summary
• We have addressed efficient processing of kNW
  queries in mobile environments.
• Our solution involves the use of our proposed
  kNR-tree.
• A single integrated index for N spatial relations
• Future Work
• Detailed performance evaluation
• Investigation of the effect of spatial density
• Load-balancing among the base stations.