Routing 2

1
Routing 2

• Outline
• Maze Routing
• Line Probe Routing
• Channel Routing
• Goal
• Understand maze routing
• Understand line probe routing

2
Maze Routing

• Place wires and components on grid
• grid size wire width spacing
• works best if all wire widths and spacings are
  equal
• grid squares occupied
• Distance metric
• each square has 4 neighbors unit cost away
• Search graph
• node for each square
• unit-cost edge to 4 neighboring nodes

3
Maze Routing

• Shortest path search (Lee-Moore)
• maintain leaf nodes of expansion tree
• at each step add unexplored neighbors to list
• with accumulated cost
• stop when target vertex reached
• backtrace for route
• Guaranteed to find shortest path
• large memory requirements - the grid
• long search time - number of vertices marked
• local optimization - only routing one net at a
  time

4
Algorithm

• add source node S into list
• costS 0
• for all nodes i on list
• if i destination D
• pathcost costD
• break
• for jN,S,E,W neighbors that are not visited and
  not occupied
• add node j to list
• costj costi1
• mark i as visited
• remove node i from list
• while i ! S do
• mark i as path
• i min cost N,S,E,W visited neighbor

5
Maze Routing

• Avoiding blockage
• wire at a time gt can block wires
• Solutions
• rip-up and re-route
• remove wire(s) causing blockage
• route blocked wire
• route ripped up wires
• shove-aside
• add dummy grid lines
• squeeze wire through

6
Line Probe Routing

• Gridless - store list of lines and obstructions
• sorted lists of vertical and horizontal lines
• Algorithm
• from source and destination project 4
  horizontal/vertical rays (probes)
• if probes intersect, done - route wires from
  nodes to intersection
• if probes blocked, choose escape point and send
  new probes
• a point just past obstruction

E
E
B
E
A
E
7
Line Probe Routing

• Advantages
• small memory requirements - no grid
• store sorted lists of vertical and horizontal
  segments
• fast
• binary search of segments for blockage and escape
  points
• probes ltlt grid points
• higher precision coordinates - no grid
• Disadvantages
• serial wire at a time - blockages
• similar rip-up and shove-aside approaches to cope
• basic algorithm may not find route when one
  exists
• need to try more escape points
• degenerates to grid search

8
Channel Routing

• Channel
• terminals on two sides of rectangle are fixed
• horizontal wires on layer1 - trunks, which run in
  tracks
• vertical wires on layer2 - branches, which run in
  columns
• Routing Problem
• minimize number of tracks used gt minimizes
  channel height
• minimize wire lengths, vias
• all wires routed at same time - better overall
  optimization

A
B
A
A
track
via
A
B
trunk
branch
dogleg
9
Channel Routing

• Left edge algorithm
• one trunk per net
• trunks on one layer, branches on other
• sort trunks by left edge
• scan trunks, put all that fit into first track
• allocate new tracks as necessary
• repeat scanning until done
• add vertical branches
• ignores vertical constraints
• can add doglegs later
• may need more tracks
• advantage
• minimum wire length, vias
• not very optimal
• 31 tracks on Deutschs difficult example
• density is 19 tracks

B
A
B
A
B
A
B
A
10
Channel Routing

• Greedy algorithm
• route column by column rather than track by track
• scan left-right by column
• at each track apply heuristics to bring new nets
  to an existing trunk, and move nets between
  tracks
• greedy - at each column try to minimize tracks
  and minimize distance to terminals
• can often use exhaustive search
• number of tracks in a column is small - lt 100
• good results, but lots of vias
• lots of track to track movement for each net

11
Algorithm

• for each column
• for each terminal bring in branch
• connect to trunk if it exists
• create trunk at first empty track
• otherwise create new track
• move between tracks using heuristics
• collapse nets to fewer trunks with spare branch
  space
• reduce distance between net trunks
• move nets towards next terminal
• connect multiple trunks for a net at end of
  channel

B
A
B
A
12
Pattern Channel Routers

• Slide window along channel
• recognize patterns of terminals and occupiedGet
  more optimal results
• doglegs
• Challenge
• developing rule set

Problem Vertical constraint between A and B. C
and D occupy surrounding tracks and
columns Solution Shift contacts down and to
right, doglegs on each layer to reach them
A
C
D
B