Routing 2

Outline– Maze Routing

– Line Probe Routing

– Channel Routing

Goal– Understand maze routing

– Understand line probe routing

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

w+s

1

1 1

1

1 1

1

1

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

16 15 14

16

16 15 1416 1516

13 12 11 10 914 1315 14 8 7

9 813 12 11 1013 12 11

15 14 1016 15 9 8

8 7 6 5 45 4 3

6 5 4 3 27 6 5 2 18 7 1 09 8 2 18 7 3 27 6 5 4 3

3 2 1 23 2 33

3 2 33 2 1 2

3 2 1 0 132 33

3

Algorithm

add source node S into list

costS = 0

for all nodes i on list

if i == destination D

pathcost = costD

break

for j=N,S,E,W neighbors that are not visited and not occupied

add node j to list

costj = costi+1

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

Maze Routing

• Avoiding blockage– wire at a time => 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

A

B

A B

A

B

A B

A

A B

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

E

A

B E

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 << # 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

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 => minimizes channel height

– minimize wire lengths, vias

– all wires routed at same time - better overall optimization

A B A

AB

Atrack

trunkbranch

via

dogleg

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 “Deutsch’s difficult example”

» density is 19 tracks

B A

A

B

B A

A

B

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 - < 100

– good results, but lots of vias

» lots of track to track movement for each net

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

BA

A

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

B

C

D