AQUASUN: an adaptable 2D range index for CAD applications

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AQUASUN an adaptable 2D range index for CAD
applications

• Michiel De Wilde
• Ghent University, Belgium

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Representation of VLSI layouts

• Complex VLSI design is done in an hierarchical
  way
• Higher-level design hierarchy persists in the
  layout phase

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Spatial searches

• In each relevant module find all relevant
  submodules
• Search operation for all window-intersecting
  layout rectangles
• In a complex module, iteration over the entire
  layout is too slow
• Auxiliary structure spatial index
• O(log(total rectangles)) time complexity for
  small windows

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Fast spatial index necessity

• Do we need a fast spatial index?

• In VLSI layout tools, several operations perform
  spatial searches
• Design Rules Check (DRC) verify minimal
  distances between, e.g., metal lines
• Parasitics extraction find close metal lines
• Graphical User Interface (GUI) find all layout
  rectangles intersecting the viewing window
• Some (interactive) operations spend substantial
  resources on spatial searches
• A fast spatial index helps to keep the
  application responsive

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Overall 2D range index approach

• Rectangle 2D interval? 2D range index
• Cope with layout changes? adaptable index

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The R-tree family

• Fully adaptable
• Generally, an efficient packing

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The quadtree family

• Applies regular hierarchical area division
• Only square nodes
• Each non-leaf node has four identical child nodes

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AQUASUN overall structure

• Adaptable quadtree skipping underpopulated levels

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AQUASUN tree composition
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AQUASUN fast adaptability

• 1 layout ? 1 optimal tree composition
• Order of adaptations is unimportant
• Subsequent adaptations? only incremental
  structural changes
• At runtime, optimal composition is upheld
• Slight intentional hysteresis? prevents
  restructuring repetitions
• Overhead of verifying optimal composition
• Almost negligible only 2..3 integer
  manipulations(in/decrements and zero-value
  checks)

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Side-by-side comparison
R-tree family
AQUASUN
Uses irregular nodes
Uses regular nodes
Only one ideal tree composition possible given
a layout
Applies heuristics to get a generally efficient
tree composition
Order of adaptations influences composition
Adaptation order independence
Depth O(log(n))
Depth ? f(n)
Non-determinism in leaf-node linking yields
adaptability overhead
Almost negligible adaptability overhead
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Performance