Coupling Aware Routing

1
Coupling Aware Routing

• Ryan Kastner, Elaheh Bozorgzadeh and Majid
  Sarrafzadeh
• Department of Electrical and Computer Engineering
• Northwestern University

2
Outline

• Coupling
• Definition
• Effects
• Coupling-Free Routing
• Definition
• Uses
• Algorithms for Coupling-Free Routing
• Greedy
• Forcing
• Results
• Conclusion

3
Coupling

• Definition - capacitance between adjacent wires
• Deep submicron trends
• Interconnect has more dominant role
• Scale wire height at slow rate compared to width

Coupling can account for up to 70 of
interconnect capacitance even in .25 micron
designs

4
Effects of coupling

• Delay deterioration
• Total capacitance seen by a gate is no longer a
  constant value
• Causes uncertainty in delay calculation
• Crosstalk
• Noise caused by coupling
• Leads to circuit failure and increased delay

5
Interconnect delay
r resistivity of the conductore insulator
dielectric constantw,t,h conductors width,
thickness and separationl, s coupled length
and spacing of interconnectDuring routing, we
can control l and s
6
How can we avoid coupling?

• Interconnect spacing
• Increasing the spacing between wires can reduce
  coupling
• Much work on this subject (Wong _at_ U. Texas, Cong
  _at_ UCLA)
• Coupled interconnect length
• Coupling directly depends on the parallel length
  of adjacent wires
• Route wires to avoid long parallel overlaps

Highly coupled
No coupling
7
Simplify definition of coupling

• Two wires couple if the segments forming them are
  closer than d units for more than l units

length gt l
distance lt d
Two wires couple if distance lt d AND length gt
l Otherwise, they do not couple
8
Coupling-Free Routing (CFR)

• Given a set of nets SNi(x1i,y1i),(x2i,y2i)
  1 ? i ? n
• S is coupling-free if there is a single bend
  layout for every net such that no two routes
  couple

Coupled layout
Coupling-free layout
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Usefulness of CFR

• Minimum interconnect delay
• Single bend routing insures minimum wirelength
• Introduces only one via
• Coupling between nets is minimized
• Increases predictability of routes
• Allows accurate prediction of wirelength,
  congestion, etc
• Predictable Routing, ICCAD 2000
• Speeds up single net routing process

10
Usefulness of CFR-Detailed Routing

• As fabrication technology progresses, routing
  layers become more plentiful
• Reserving layers for critical nets is common
• Power, ground and clock are already routed on
  preferred layers
• Use preferred layers for critical nets
• Layer can be used for timing critical nets
• Critical nets have little slack - need minimum
  delay
• CFR insures that nets have minimum delay
• minimum wirelength
• minimum number of vias
• minimum coupling

11
Usefulness of CFR-Single Layer

• Single layer routing is a important problem for
  routing
• Area routers often use single layer routing for
  each layer
• Printed Circuit Board (PCB) use single layer
  algorithms
• Best known academic single layer router
  (developed by Lin and Ro) uses two step process
• Find a maximum planar set of one-bend nets
• Use rubberband equivalent to route remaining nets
• CFR can be easily be incorporated into in first
  step to
• produce a planar set of nets with minimum coupling

12
Usefulness of CFR-Global routing

• Coupling at global routing is hard to determine
• Routes are not exact, makes it difficult to know
  adjacency relations of nets
• Detailed router will often make local changes
• Global routing allows global changes, it is next
  to impossible to make global changes at the
  detailed stage
• A coupling-free global layout will produce a
  coupling-free detailed layout

13
MAX-CFL Definition

• Given a set of two-terminal nets S and a positive
  integer K ? S. Is there a single bend routing
  for at least K nets such that no two routings
  couple?
• Additional routing constraints can easily be
  added
• Routed nets must be planar
• Routed nets must be routed on two layers
• MAX-CFL for planar layouts is NP-Complete
• General MAX-CFL NP-Complete?

14
Algorithms

• We developed two algorithms
• Greedy
• Forcing
• Algorithms try to maximize number of nets routed
  and/or criticality of routed nets

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Criticality

• Most often defined as the amount of timing slack
  available for the net
• Slack values given gates, nets during logic
  synthesis stage
• Delay through a network of gates and wires must
  not exceed clock frequency

gate
Flip Flop
gate
Flip Flop
gate
network
DSM increases for need interconnect timing
slack
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Results in terms of criticality

• Benchmarks do not have criticality data
• We used wire length for criticality
• Delay increases at rate
• O(l2) without wiresizing
• O(l?l) with optimal wiresizing
• O(l) with proper buffer insertion
• We ran experiments using each function as
  criticality

Criticality functions Quadratic (l2), l-root-l
(l ? l) and linear (l) functions
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Greedy Algorithm

• 1 Given a set of nets N
• 2 Sort N by criticality (largest ? smallest)
• 3 for each net n ? N
• 4 do route n in upper-L or lower-L, if
  possible
• Simple and fast Running time is O(n log n)

18
Forcing algorithm

• In order to avoid coupling, a routing of a net
  forces another net into a particular route

Net 1
Net 1
To avoid coupling Net 2 must be lower-L
Net 2
Net 2
An lower-L routing of Net 1 forces a lower-L
routing of Net 2
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Forcing Algorithm

• 1 Given a set of net N
• 2 Determine the forcing interactions between the
  nets ? N
• 3 R ? NULL
• 4 for each net n ? N
• 5 do R ? R U n.upper-L U n.lower-L
• 6 Sort R by number of forcings (smallest ?
  largest)
• 7 for each routing r ? R
• 8 do if net associated with r is unrouted and
  r is routable
• 9 then route r

Running time is O(n2)
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Evaluation

• Find the x most critical nets in each circuit
• Vary x from 25 to 250
• Perform algorithms on the x nets
• Gathered statistics from each layout
• Percentage of nets laid out
• Criticality of nets laid out

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Circuit Benchmarks
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Fraction of nets placed
Forcing algorithm outperforms greedy algorithm
23
Forcing vs. Greedy
relative criticality (greedy criticality)/(forci
ng criticality)
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Criticality results

• Greedy algorithm outperforms every other function
• Using linear function 20 better than forcing
  algorithm
• l-root-l and quadratic functions have similar
  trends

Greedy algorithm best for criticality
25
Conclusion

• Coupling-free routing useful for many routing
  algorithms
• Detailed routing
• Global routing
• Single layer routing
• Allows early prediction of routing metrics
• Congestion
• Wire length
• Interconnect delay
• Implication algorithm maximizes routes placed
• Greedy algorithm maximizes criticality placed