Improving Spatial Data Processing by Clipping Minimum Bounding Boxes - - PowerPoint PPT Presentation

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Improving Spatial Data Processing by Clipping Minimum Bounding Boxes - - PowerPoint PPT Presentation

Jun 16, 2023 153 likes •452 views

Improving Spatial Data Processing by Clipping Minimum Bounding Boxes Darius Sidlauskas Sean Chester EPFL NTNU Eleni Tzirita Zacharatou Anastasia Ailamaki EPFL EPFL Br Brain mo model el (axons) 97% of the Minimum Bounding Box is empty

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SLIDE 1

Improving Spatial Data Processing by Clipping Minimum Bounding Boxes

Anastasia Ailamaki

EPFL

Darius Sidlauskas

EPFL

Sean Chester

NTNU

Eleni Tzirita Zacharatou

EPFL

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SLIDE 2

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97% of the Minimum Bounding Box is empty

Br Brain mo model el (axons)

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SLIDE 3

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Up to 64% of the accessed leaf nodes are false hits

Empty space ce è unnece cessary I/Os Os

Query 20 40 60 80 100 High Medium Low Query Selectivity Optimal/Actual #leafAcc (%)

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SLIDE 4

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Tighter struct cture (convex hull)

Empty space from 97% to 37%, but requires 49+ points

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SLIDE 5

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Ho How t w to r

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educe d e dea ead sp space wi e with th on

  • nly f

few e w extr tra p poi

  • ints

ts

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SLIDE 6

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“Li “Light cuts” ” using only few extra points

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SLIDE 7

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45% reduction in empty space with just 3 extra points

“Li “Light cut cuts” us using o ng onl nly f few e w extra po points

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SLIDE 8
  • Relevant to a corner of the Minimum Bounding Box.
  • The rectangular area between the clip point and the

corner is dead.

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Cl Clip point

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<p2,00> <p3,00>

Low representation overhead for clipped areas

R11 <p1,11> R00

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SLIDE 9
  • Augments the Minimum Bounding Box with a set of

clip points.

  • The lesser the retained volume, the better the

approximation.

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Cl Clipped ed Bo Bounding g Bo Box (CBB) CBB)

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<q,11> <t,00> R11 R00 <p,11>

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Challenge: Choice ce of cl clip points

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Choose ≤ k clip points that maximize the eliminated volume

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Candidate cl clip points

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R00

  • For given corner Rb:
  • Consider only points in the outer surface of the objects oi.
  • Consider only the closest corner oib.
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SLIDE 12

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Candidate cl clip points

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R00

  • For given corner Rb:
  • Consider only points in the outer surface of the objects oi.
  • Consider only the closest corner oib.
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SLIDE 13

Sk Skyline e cl clip points

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R00

  • For given corner Rb:
  • Consider only points in the outer surface of the objects oi.
  • Consider only the closest corner oib.
  • Only the clip points in the Skyline of {oib} are valid clip

points!

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Sk Skyline-ba based d CBB

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R00 R11 R10 R01

  • Get skyline points with respect to each corner Rb.
  • Choose up to k points.
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SLIDE 15
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Sk Skyline-ba based d CBB (k k = 1 = 1)

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SLIDE 16

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Sk Skyline-ba based d CBB (k = 2 = 2)

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SLIDE 17

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Sk Skyline-ba based d CBB (k = 3 = 3)

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SLIDE 18
  • “Between” two skyline points.
  • Retain the “best” value in each dimension.
  • Clip away significantly more dead space.
  • Require more expensive pre-processing.

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St Stairline cl clip po points ts

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R11 q p

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St Stairline-ba based d CBB CBB

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R11 R00 R10 R01

  • Get stairline points that are valid clip points with

respect to each corner Rb.

  • Choose up to k points.
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SLIDE 20
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St Stairline-ba based d CBB (k k = 1 = 1)

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SLIDE 21
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St Stairline-ba based d CBB (k k = 2 = 2)

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SLIDE 22
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St Stairline-ba based d CBB (k k = 3 = 3)

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SLIDE 23
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St Stairline-ba based d CBB (k k = 4 = 4)

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SLIDE 24
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St Stairline-ba based d CBB (k k = 5 = 5)

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SLIDE 25
  • R-tree variants Quadratic [QR-tree], Hilbert [HR-tree], R*-tree,

Revised R*-tree [RR*-tree]

  • Range queries
  • High: ≈ 1 object per query
  • Medium: ≈ 10 objects per query
  • Low: ≈ 100 objects per query
  • Hardware Quad-core Intel Core i7-3770 CPU @ 3.4GHz, 16GB RAM,

500GB HDD - 7200RPM

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Ex Experimental Setup

rea02 ~2M elements axo03 ~2.5 M elements par02/par03 230 elements

  • Spatial Join
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SLIDE 26

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Dead space ce el elimi mination

CBBs remove 27% - 60% of dead space

Stairline clipping Dead space / node volume (%) QR-tree HR-tree R*-tree RR*-tree Dead space:

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SLIDE 27

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Range query performance ce

Selectivity: high medium low

≈26% I/O reduction across all R-trees/workloads

  • Avg. #leafAcc w.r.t. original (%)

QR-tree HR-tree R*-tree RR*-tree Stairline clipping

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SLIDE 28

Querying 1B spatial object cts

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  • Avg. query time (sec)

par02: 71 GB par03: 91 GB

Enabling interactive times for 1B objects

Selectivity: medium RR*-tree Original Skyline-clipped Stairline-clipped HR-tree

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SLIDE 29
  • The Minimum Bounding Box (MBB) is ubiquitous
  • Compact
  • Cheap intersection tests
  • Poor approximation of real data: can be > 90 % empty

è up to 64% unnecessary I/Os!

  • The Clipped Bounding Box
  • Augments the MBB with few additional clip points
  • Retains the simplicity of the MBB
  • Eliminates up to 60 % of dead space
  • Enables interactive exploration of 1B objects

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Ta Take home message Th Than ank you

  • u!