On-Line Discovery of Hot Motion Paths

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On-Line Discovery of Hot Motion Paths

• D. Sacharidis1, K. Patroumpas1, M. Terrovitis1,
• V. Kantere1, M. Potamias2, K. Mouratidis3, T.
  Sellis1
• 1National Technical University of Athens, Greece
• 2Boston University, U.S.A.
• 3Singapore Management University, Singapore

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outline

• problem formulation
• example
• motion paths
• definition, example
• system setting
• naïve method
• our approach
• RayTrace algorithm
• SinglePath strategy
• experiments
• conclusions

3
problem

• identify hot motion paths followed by moving
  objects over a sliding window with guarantees
• motion path
• a directed line segment approximating objects
  movement
• hotness
• number of objects crossing a motion path within
  the window
• guarantees
• user-defined tolerance e for approximating the
  location of an object at a given time
• challenges
• line segments are not known in advance, may
  change over time
• unlike counting frequencies of spatial areas
• find good motion paths long and hot

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problemexample

• consider 4 moving objects and their trajectories
• assume tolerance e in approximating positions
• extract motion paths
• calculate hotness
• select hottest (hotness ? 2)

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motion pathdefinition

• given tolerance e a motion path papb is a
  directed line segment with the requirement that
• the motion path is a bounded piecewise linear
  approximation of the objects movement at some
  time interval
• there exists a time interval ta, tb such that
  for every ? ? 0, 1 the point p(?) pa
  ?(pb-pa) is within distance e to some objects
  location at time ta ?(tb-ta)
• a motion path fits an objects movement and an
  object crosses a motion path
• a set of motion paths is covering for an object
  if at any time the object crosses exactly one of
  its paths

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motion pathexample
consider the trajectory of a single object moving
in x assume tolerance e consider four motion
paths the red ones are covering
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system setting

• objects
• move freely
• have location aware devices (GPS,
  cell-tower/wifi-antenna triangulation) with
  varying degrees of inaccuracy
• limited processing ability and scarce battery
  life
• communication channel with central coordinator
• coordinator
• full processing ability
• communication channel with every object

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finding hot motion paths

• naïve method
• every object sends all its location updates to
  the coordinator
• too much communication overhead gt drains battery
  life
• the coordinator exhaustively tries to fit the
  best motion paths
• too much processing cost on a single site
• our two-tiered approach
• RayTrace algorithm
• simple low-cost algorithm that acts as a
  spatio-temporal filter
• only when the object falls outside the filter an
  update occurs
• SinglePath strategy
• motion path discovery algorithm using lightweight
  indexes
• processes objects updates
• sends feedback to objects at predefined epochs

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RayTraceoverview

• executed by each object independently
• modest requirements
• one-pass over streaming location updates
• constant time (per update) and constant space
• maintains a Spatio-temporal Safe Area (SSA)
• SSA guarantees that a valid motion path exists
• when the object falls outside the SSA
• a motion path must be assigned for the previous
  time interval
• a message is sent to the coordinator with the
  current state
• feedback is received during the next epoch and
  RayTraces starts over with a new SSA
• subsequent location updates are buffered

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RayTraceSSA

• positional updates are timepoints (locations with
  timestamps) accompanied with the measurement
  inaccuracy ltpi, ti, eigt
• for simplicity assume a fixed tolerance e for all
  errors
• the extension to varying errors is
  straightforward
• the case of handling uncertainty (e,d) is
  presented in the paper
• SSA is a spatio-temporal pyramid-like area
  defined in the xyt space that extends
• from an anchored initial timepoint (provided by
  the coordinator as feedback)
• to a rectangle at the current timestamp
• SSA is updated/redefined at each timepoint

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RayTraceupdating the SSA

• consider an initial timepoint ltp0, t0gt
• timepoint ltp1, t1gt arrives defining a square Q1
  of side 2e around it
• SSAs end rectangle becomes this square
• next timepoint ltp2, t2gt with rectangle Q2
  arrives
• SSA is expanded up to timestamp t2
• the end rectangle is produced by the intersection
  of the old with Q2
• if the intersection is empty a message is sent to
  the coordinator

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SinglePathoverview

• the coordinator receives updates from objects
• executes the SinglePath strategy to extract a
  motion path for each reporting object
• may choose an already seen motion path or create
  a new one
• informs each object about the selected motion
  path
• SinglePath uses lightweight indexes
• a spatial index for storing the motion paths
  discovered
• grid indexing motion path edges
• a hash table for storing the hotness of each
  motion path
• an event queue for handling sliding windows
  evictions
• if an object crosses path j at time t, an event
  lttW,jgt is en-heaped
• the event with the lowest timestamp tlow is
  always de-heaped and processed when the current
  time is greater than tlow

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SinglePathprocessing updates

• objects send their states when they fall outside
  the SSA
• state is the last valid SSA
• the initial timepoint
• the end rectangle
• coordinator chooses a motion path based on
  SinglePath
• must lie completely inside the SSA
• reuse motion paths as much as possible gt hotter
  motion paths
• the problem reduces to
• find a good endpoint inside the end rectangle
• always choose the hottest among candidates

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SinglePathselecting good motion paths

• a range query is issued in the grid for each end
  rectangle
• two cases may occur

(2) there are some (maybe 0) startpoints inside
the rectangle consider intersections from other
rectangles introduce artificial points
(1) there are motion paths with the same
startpoint and with endpoint inside the rectangle
choose hottest motion path
choose hottest startpoint
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experiments

• objects moving on the road network of Athens
• 1000 nodes, 2000 edges
• objects randomly assigned to a node
• objects move with an agility probability 10
• move at equal displacements, 10 meters
• follow high traffic roads more frequently
• reported positions have fixed error 1 meter
• simulation parameters
• total 250 timestamps
• window 100 timestamps
• epoch 10 timestamps
• 10,000 to 100,000 objects
• tolerance 1 to 20 meters

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experiments

• competitor
• we use an adapted streaming Douglas-Peucker
  algorithm for compressing trajectories within
  tolerance
• when the tolerance is exceeded a new motion path
  is inserted
• try to find few good segments, perform a range
  query around each endpoint augmented by the
  tolerance
• this violates the motion path requirements
• discovered segments are not motion paths
• an indication of how well our method performs
• measures
• efficiency we measure the size of the index
• how many motion paths are discovered
• quality we measure how large and hot paths are
• score hotness length

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experiments

• index size versus
• number of objects
• tolerance

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experiments

• score of the top-10 hottest segments versus
• number of objects
• tolerance

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experiments

• epoch processing time versus
• number of objects
• tolerance

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conclusions

• presented a two-tiered approach for discovering
  interesting movement patterns
• experimentally verified the handling of
  uncertainty and the discovery of an unknown road
  network
• future work
• objects learn more about current motion paths
• coordinator sends spatial information stored to
  objects

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thank you!http//web.dblab.ntua.gr