A Negotiated Congestion based Router for Simultaneous Escape Routing

Q.Ma, T.Yan and Martin D.F. WongDepartment of Electrical and Computer EngineeringUniversity of Illionis at Urbana-Champaign, USA

ISQED 2010

Outline

Introduction Problem Formulation Underlying Routing Graph Negotiated Congestion Application on Bus Untangling Experimental Results Conclusion

Introduction

PCB routing is the problem of determining wiring connections between pin terminals on the circuit board.

This paper focuses on a key problem in PCB routing called escape routing.

The objective of escape routing is to route all terminal pins inside a component to the component boundaries.

Introduction

There are several types of escape routing problems: Single-component escape: route all pins inside a

component to the component boundary without any constraint on the pin ordering

Ordered escape: one component, require the escape routing to conform to specified ordering along the boundary

Simultaneous escape: two components, the pin orderings of the escape routing for the two components are required to match each other in order to provide a planar topology for later detail routing between the components

Introduction

Problem Formulation

Each routing tile has a horizontal capacity, vertical capacity and a diagonal capacity.

cap(2,2,3) denotes the horizontal, vertical and diagonal capacities of a tile are 2, 2 and 3.

Problem Formulation

Input: Two components and the net number n, each component

is a rectangular pin grid

Objective: Obtain detailed routing from these pins to the boundaries

so that ordering of the escaped pins along two components’ boundaries match each other.

The escape routing inside the components is also required to satisfy the capacity constraints.

Underlying Routing Graph

Graph model for a tile Each node in this graph model can only accommodate

one net. (the node capacity is 1)

Underlying Routing Graph

cap(2,2,3)

Underlying Routing Graph

This graph model correctly captures cap(2,2,3)

Underlying Routing Graph

It can be easily modified to model the tile with cap(2,2,4)

Underlying Routing Graph

The entire routing graph

Negotiated Congestion

The negotiated congestion based routing scheme has been widely used in FPGA routing and global routing.

In this routing scheme, routability is achieved by forcing all the nets to negotiate for a resource.

Determine which net needs the resource most.

Negotiated Congestion

The cost of a node v is computed by the following formula:

bv: the base cost hv: the history cost pv: the number of nets currently occupying node v

Negotiated Congestion

Initialize the cost

Increase the history cost by Δ

Every net is rip-up and reroute

Increase Δ

Application on Bus Untangling

Bus untangling problem: Given two columns of pins with labels {1..n} on each

column Detour the pins to make the ordering match in the

middle. The detouring must also satisfy the capacity

requirement between adjacent pins in each column.

Application on Bus Untangling

Two sides untangling can redistribute the occupied vertical tracks to two sides so that the max number of vertical tracks used on one side is reduced.

Application on Bus Untangling

Some inputs may not have single detour solutions.

3

4

2

1 3

4

2

1 3

4

2

1 3

4

2

1

Application on Bus Untangling

View the bus untangling problem as a special case of the escape routing problem.

Each pin column constitutes a component.

Since NCER allows detours anywhere, the solution can have detours on both sides.

Experimental Results

Experimental Results

Experimental Results

Conclusion

This paper studies the feasibility of applying negotiated congestion routing scheme to simultaneous escape routing problems.

The two routers exhibit complementary behaviors.