Improved Global Routing through Congestion Estimation

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Improved Global Routing through Congestion
Estimation

• Raia T.Hadsell, Patrick H.Madden

Presented by Ori Vinik
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Reminder

• Stages in making a chip
• Defining requirements
• Logical (RTL)
• circuit design (gate level)
• Validation
• Layout
• Placement
• Routing (global)
• Routing (detail)
• And so on

• Routing wires on the chip is done using
• a tool called router

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Outline

• Introduction of the problem and some technical
  terms

• Previous work that was done in the routing field

• The routing tool created by the writers of this
  
• article and the new approach it utilizes

• Illustration of the approach

• Experimental results

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Introduction

• After placing all the components on the chip the
  next
• stage is connecting them with wires

• Short wires improves chips performance

• If routing is done simply in the shortest path
  many
• wires will be routed through important
  junctions

Looking at the chip from above
Components (ALU, registers unit)

• Congestion when too many wires go through a too
  
• narrow space physically they become too close.
• Impossible to route because capacity is limited!

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• Congestion example

No other wire can be put in this place
Wire
No more room!

• Another problem that was created

• When two wires go side by side, they effect each
  
• other so the signals might change

• The longer they go side by side, the more intense
  
• is their influence on each other

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• Some terms

• Global router decide roughly where wires will
  go through
• according to placement and other limitations
• (wires not too close, wire length).

• Maze router using for Detailed routing
  decide
• exactly where wires will go through according
  to the
• global routing.

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• Some more terms

• Rip up and reroute a common method routers
  utilize the
• router first rip an old wire, can put a new
  wire in the old
• wires place and then find a new route for the
  old wire

• Iterations in every iteration rip up and re
  route is done
• Feedback is given to the router after each
  iteration

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• Some more terms

• Routing layers most modern chips have 5 to 8
  metal
• layers in which wires are routed. These wires
  are using
• to connect the components on the chip. In each
  layer
• wires go from east to west or south to
  north.

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• A side view (abstract)

isolation layer
Routing Layers
Via
Wires
Components
Substrate
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• The past

• In the past chips were relatively simple
• Routing problem could be solved easily

A simple case with a simple solution-
But
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• As designs became bigger and more complicated

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• The problem

• Designs have become larger and more congested,
• global routing is more difficult.

• Many existing global routing tools

• Unacceptably long time

• Fail to complete - they need more area

• Problem is NP - hard

• Exponential complexity or higher

• Must use approximation algorithms to
• get practical solutions

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Guidelines

• Utilization of Linsker method for printed
  circuit board
• (PCB) routing (overlooked).

• Feedback loop to each rip up and reroute
  iteration.

• Informing the maze router in order to avoid
  congested
• areas.

• How do we determine the congested areas? (2 ways)
• Static probabilistic algorithm
• Dynamic information about congestion from
  previous
• iterations

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• Guidelines cont

• The information is used to introduce artificial
  weight to
• the congested edges

• Subsequent routes disperse from this areas in
  next reroute

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Quick summary

• Wires must have a minimal distance between them
  
• to ensure they dont short

• Routing problem in complex designs

• Modern Global Routing method terms

• Congestion

• Global router

• Maze router

• Over the cell routing

• Routing layers

• Iterations of Rip up and reroute with Feedback

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Previous work

• In the past- channel based , limited number of
  
• routing layers

• Connection restricted between standard cell rows
• or around macro blocks

• Over the cell routing instead of using space in
  cell rows

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• Formulation of modern routing model problem

• In the modern routing model problem is
  formulated
• as a Multi commodity flow

• A graph G(V,E) is given

• Each edge e between vertices V

i
I,j
and V has a capacity C
j
I,j

• Reduction

flow on the edges
wire
Component( )
vertex
edge
Route (connection between squares )
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• The common technique in previous routing tools

• Decomposition of multipin nets into pairs of pins
• using either Spaning tree algorithms or Steiner
  Tree
• heuristics

• In general The problem Connect vertices
  (1,2,3,4,5)
• becomes connect (1,2), connect (2,3) and so
  on

• Pairs of pins are connected (routed) using the
  maze
• router. Normally, Dijkstras algorithm is used

• Routing is done through iterations of rip up
• and reroute

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• Steiner Tree

• Forming a Steiner tree to connect subsets of
  vertices
• such that capacity rules must be obeyed,
  minimizing
• total tree weight

(1,2) (2,3) (2,5) (5,6) (6,9) (5,4) (7,8)

• Manhattan only

Connect (1,2,3,4,5,6,7,8,9)
Connect
Steiner tree algorithm
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1
2
3
1
2
Connect
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5
6
4
5
6
7
8
9
7
8
9
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• Dijkstras algorithm

• Dijkstras algorithm An algorithm to find the
  shortest
• path from a single source vertex to all other
  vertices
• in a weighted, directed graph. All weights must
  be non
• negative

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4
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D
1
3
2
1
10
8
10
12
3
4
2
3
2
10
2
2
9
4
9
5
S
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• Routing capacity

• In previous research it was found that detail
  routing become
• difficult when routing approaches physical
  capacity

• The detail routing is using Dijkstras algorithm
  and determine
• the exact and final routing, complimenting the
  Global routers
• work

detailed router
Global router

• Thus, the capacity of an edge in a global graph
  is generally
• tuned towards levels where successful detail
  routing is likely

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Global Routing with Congestion Estimation

• The Chi Dispersion Global Routing tool routing
  approach
• extends previous work (Linsker) through the
  introduction of
• congestion estimation.

• Basic routing approach follow the general
  outline of
• Linsker

• Decompose multi-pin nets into sets of point
• connections, and then route each connection

• Use of Steiner tree heuristic obtaining good
  quality
• trees and low complexity

• Each wire (in the tree) is routed using a maze
  router,
• implementing Dijkstras algorithm ensure
  efficient
• implementation

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• The Chi Dispersion Global Routing tool

• Rip up and reroute each edge in order for a
  number
• of iterations

• Why for a number of iterations?

• Solution converges quickly. Large number of
  iterations
• seldom improve quality

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• Edges Weights

• In order to implement Dijkstras algorithm
  adjusting
• routing cost (weight on the edges) is a must.

• How is this done?

• Monitoring the number of routes (wires) using
  any
• particular edge and use this to adjust routing
  cost as
• demonstrated in next foil

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• Adjusting routing cost using a cost function-
• example

route
Wire Need 25
Capacity 120
Step 1 Routing cost LOW
Step 3 Routing cost Medium
Step 4 Routing cost High
Step 2 Routing cost LOW

• important this is just one algorithm. Other
  Possibility
• LOW,LOW,LOW, HIGH or others. Depends on cost
  function.

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• The cost functions

• Step cost function

• Routing cost increases abruptly when
• the number of routes on a graph edge
• reaches or approaches the edge
• capacity.

constant
if any
wire length
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• Intuition for the step cost function and the
• problem it creates

• Early routes will encounter an uncongested
  routing graph
• and will utilize the resources without
  consideration for the
• demands of later routes (A).

B

• Later routes will not be able to go through
• that congested edge routing cost
• is too expensive (B). They will detour
• around congested regions

A

• During rip up and reroute, the connection routed
  in early
• stages will have difficulty in being rerouted,
  because of the
• added wire length.

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• The main problem with this approach

• Prior to initial routing no information about
  where
• congestion is going to be

• As a result first routes might pass through
  areas that will
• have high demand later

• These routes will affect the routing of other
  wires

• The objective minimizing the number of poorly
  routed
• connections in the early stages. And providing
  an
• effective tie-breaking method when there are few
  routes
• with similar costs.

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• The effective cost function

• Linear cost function

• Assign a unit cost to an edge until it reaches
  80 of capacity (A) and increase cost linearly
  until it reaches 40 above capacity (B) .

• Why 40 above capacity?

B
A
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• Intuition for the linear cost function

• If a region is about to be congested (over 80 of
• capacity) routing cost is rising
• The routing cost will rise as more and
• more wires are routed through that edge
• As rip up and re route process is performed the
  Dijkstras
• algorithm will route some wires through other
  edges, living
• some room for later routes that will willing to
  pay the
• high routing cost through that edge

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• Technically how does it work?

• The amplified dynamic demand for routing edge ej
  is

ddynamic(ej) S a(wi) X p(wi,ej)
wi
According to next page
The probability that wi will be routed through
edge ej
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• Technically how does it work?

• Amplification algorithm
• For any given wire wi, consider the estimated
  demand along all routing edges used by the wire
• If no routing edge has demand greater then 80 of
  capacity, we set a wi to 0
• If a routing edge demand greater then 120 of
  capacity, we set a wi to 1.2
• Otherwise, a wi is set to 1

ddynamic(ej) S a(wi) X p(wi,ej)

• The dynamic estimation is performed once per
  iteration.
• The static estimation is performed prior to any
  routing.

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• Observations

• In heavily congested areas there is desire to
  push
• routes out. Routing there should cost much more
• In lightly congested areas we want to avoid
  detours

• What did we get?

• Strongly influence routes in congested areas
  without unduly influence routes in less congested
  areas

• Volcano effect the areas where we would
  expect heavy
• congestion have routes strongly pushed away

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• The process - overview

Static estimation
Routing cost
dynamic estimation
amplification
Actual routing Demand
Dijkstra
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• Contribution of this work

• The consideration of congestion estimate as part
  of the
• routing cost

• Static and dynamic congestion estimates

• Combination of both provide a hint to the
  global
• router

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Illustration of the Approach

• Congestion maps
• Lightly congested dark
• Heavy congested light

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• congestion maps illustration of the approach

• Estimated congestion and amplified estimated
  congestion
• for the benchmark IBM01.

After global routing is done
Left congestion estimate for ibm01 Right
amplified congestion estimate for ibm01
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• Illustration of the approach different
  iterations

• Congestion levels for a routing of the benchmark
  IBM07 at
• different iterations of the rip up and reroute
  process.

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• What did we see?

• Congestion levels in the first iteration is much
  higher in the
• congestion prediction approach

• After first iteration congestion levels improve
  dramatically.

• Our modified approach performs substantially
  better

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Experimental results

• Executable versions of only two academic routers
  were
• available
• Labyrinth
• Force Directed router

• The Force Directed router was unable to handle
  any of the
• given benchmarks correctly

results not reported.

• Commercial routing tools are not comparable since
  they
• generally optimize a number of factors other
  then
• congestion.

• About Labyrinth

• Use Rip up and Re-route

• Using step function

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Experimental results cont
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• Results in different benchmarks

overflow
overflow
overflow
On average, 47 overflow reduction relative to
Linsker On average, 65 overflow reduction
relative to Labyrinth Wire length and run time
are comparable to Linsker, better than Labyrinth
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Summary / Conclusions

• Focus on improving congestion in global routing
  using
• over-the-cell routing model

• This work improves a classic routing approach by
• integrating congestion estimates with the routing

• Target problem areas without introducing
  detours
• in un congested areas by amplifying estimated
  
• congestion

• Excellent results in comparison to other recent
  global
• routing work speed, wire length, overflow

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Summary / Conclusions cont

• A method known for printed circuit board design
  has a
• direct application to modern integrated circuit
  routing

• Use of a linearly increasing cost function
  improves the
• solution quality

• Some recently published routing tools have
  surprisingly
• poor performance and may be improved by adopting
  this
• approach

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Acknowledgements

• IEEC AND IBM Faculty Partnership Award

• Ralph Linsker - IBM

• Shaodi Gao - IBM

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the end
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• Steiner Tree

• Problem definition

Given a graph with non negative weights and a set
of pairs of vertices, find the minimum network of
edges such that each pair of vertices is in the
same connected component.

• Manhattan only

• Forming a Steiner tree to connect subsets of
  vertices
• such that capacity rules must be obeyed,
  minimizing
• total tree length

Steiner tree algorithm
Connect