Predictable Routing

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Predictable Routing

• Ryan Kastner, Elaheh Borzorgzadeh, and Majid
  Sarrafzadeh

ER Group Dept. of Computer Science UCLA Los
Angeles, CA
NuCAD Group Dept. of Electrical Computer
Engineering Northwestern University Evanston, IL
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Outline

• Pattern Routing
• Predictable Routing
• Experiments
• Smallest First Pattern Routing
• x-density Pattern Routing
• Wire length and Run time
• Conclusion

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Pattern routing

• Use simple patterns to connect the terminals of a
  net
• Simplest pattern is single bend routing
• Given a two-terminal net, single bend routes are
  the two distinct 1-bend routes
• Sometimes called L-shaped routing

• There are many other types of patterns
• We focus exclusively on L-shaped patterns

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Why use patterns?

• Faster routing
• Number of bin edges searched

• Maze Routing O(E) all edges in Grid Graph
  275 bin edges

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Why use patterns?

• Small wire delay
• The route has minimum wire length
• Only one via introduced
• Minimal interconnect resistance and capacitance
• Fewer number vias ? fewer detailed routing
  constraints

• Downside may degrade quality of routing
  solution
• Maze routing will consider every possible path
• L-shape routing considers 2 paths

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What is Predictable Routing?

• Definition Pattern route a subset of critical
  nets

Critical Nets pattern route
Non-critical Nets maze route

• Benefits
• Wire planning - Organizes routing
• Important routing metrics more accurately modeled
  a priori
• Congestion
• Wire length

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Predictable Routing

• Number of patterns should be small
• Fewer patterns ? higher route predictability

50 chance for upper-L
50 chance for lower-L
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Experiments

• Focus on pattern routing critical nets
• Criticality label by high level CAD tools
• Criticality increasingly dependent on wire length
• Goal Show that you can pattern route critical
  nets without degrading the routing solution
  quality
• We focus on routability
• Wire length, run time considered as secondary
  factors

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Benchmark circuit information

• 5 MCNC standard-cell benchmark circuits
• Unfortunately, benchmarks provide no criticality
  data

Need to find heuristics for pattern routing
small and large nets
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Criticality Heuristics - SFPR

• Smallest-First Pattern Routing (SFPR)
• Sort two-terminal nets based on BB (smallest to
  largest)
• Pattern route x of the smallest nets
• Maze route remaining nets
• Rip up and reroute phase
• Do not consider the pattern routed nets
• SFPR focuses on pattern routing small critical
  nets

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SFPR results

• Results are the total overflow (measure of
  congestion)
• Smaller is better (min overflow min congestion)
• 70 of the small nets can be pattern routed

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Pattern routing long nets

• Pattern routing longest nets first leads to large
  degradation in quality of routing solution
• Idea choose long nets that are evenly
  distributed across the chip
• x-Density routing
• Every edge of the grid graph has at most x nets
  crossing it

• Example of a 1-density routing

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x-Density Routing

• Formal definition decision problem
• Given an integer x, a set of two-terminal nets N
  and a grid graph G(V,E)
• Does there exist a single bend routing for every
  net ni in N
• 1 lt i lt N such occupancy(e) ? x for every edge
  e ? E?
• Polynomial time solvable - O(N log N) time
• Finding the maximum subset of nets is much harder

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x-Density Pattern Route Heuristic (x-DPR)

• The x-DPR heuristic
• Find a set of x-Density routable nets
• Set should be x-Density with large nets
• Pattern route the x-Density nets
• Maze route the remaining nets
• Rip and reroute nets
• Do not consider the x-Density nets

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x-DPR results

• x-density (x ? 3) routing does not degrade
  routing solution
• Allows large nets to be routed

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Wire length and Run time

• Wire length
• Pattern routed (critical) nets guaranteed to have
  minimum wire length
• Overall wire length varies over benchmarks 5
  to 10
• Run time
• Single Net Pattern routing faster (lower
  theoretical upper bound)
• Overall global routing
• Pattern routing nets adds restrictions ? small
  solution space
• Rip up and reroute phase may take longer to find
  a better solution
• Running time trends
• SFPR Small circuits 20 worse with pattern
  routing
• SFPR Large circuits overall runtime similar (
  5) or better
• x-density overall runtime similar ( 5)

Sometimes there is small degradation in wire
length and run time
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Conclusions

• We showed that you can pattern route up to 70 of
  small nets
• We showed that you can pattern route large nets
  using x-density routing
• We showed that pattern routing has many benefits
• Better prediction of routing metrics
• Pattern routed nets have small interconnect delay
• Allows early accurate buffer insertion, wire
  sizing and wire planning