A Topology-based ECO
Routing Methodology for
Mask Cost Minimization
Po-Hsun Wu, Shang-Ya Bai, and Tsung-Yi Ho
Department of Computer Science and Information Engineering, National
Cheng Kung University, Tainan, Taiwan , ASPDAC,2014
OUTLINE

I. INTRODUCTION

II. TILE-BASED ROUTING GRAPH CONSTRUCTION

III. ECO ROUTING WITH MASK COST MINIMIZATION

IV. NETWORK FLOW-BASED ECO ROUTING
REFINEMENT

V. EXPERIMENTAL RESULT

VI. CONCLUSION
INTRODUCTION

With the rapid evolution of process technology
over the last decade, more complicated design
complexity becomes inevitable.

As the design complexity becomes more
complicated, more circuit failure and constraint
violations may occur during later design stage due
to increasing design rules.
INTRODUCTION

Engineering Change Order (ECO) technique is
proposed to keep transistorlayer masks intact and
only re-spin the less expensive metallayer masks
to perform incremental design changes.
INTRODUCTION

[8] presented a tile-based ECO router to improve
total wirelength and used vias.

[9] proposed a topology-aware buffer insertion
and GPU-based massively parallel rerouting
methodology to maintain circuit performance.

[5] developed a redundant-wires-aware ECO
approach to improve circuit timing and reduce
the number of changed masks.

Since no ECO router can globally optimize
different ECO nets to minimize the number of
changed masks, we propose a new ECO routing
flow that is capable to finish ECO routing while
reducing total number of changed masks.

I. TILE-BASED ROUTING GRAPH CONSTRUCTION

II. ECO ROUTING WITH MASK COST MINIMIZATION

III. NETWORK FLOW-BASED ECO ROUTING
REFINEMENT
TILE-BASED ROUTING GRAPH CONSTRUCTION

The tile-based routing graph can be constructed
by extending lines through the boundaries of all
obstacles until they intersect with other obstacles
or the boundaries of other routing regions, where
each tile is represented by a respective node and
an edge between two nodes indicates two tiles
are adjacent.
TILE-BASED ROUTING GRAPH CONSTRUCTION

All adjacent tiles with vertical (horizontal)
routing direction are horizontally (vertically)
merged, then the maximum
horizontally/vertically stripped (MHS/MVS) tiles
are applied for the layers with vertical/horizontal
routing direction.

I. TILE-BASED ROUTING GRAPH CONSTRUCTION

II. ECO ROUTING WITH MASK COST MINIMIZATION

III. NETWORK FLOW-BASED ECO ROUTING
REFINEMENT
ECO ROUTING WITH MASK COST
MINIMIZATION

The proposed ECO routing algorithm contains
three major steps.

Initially, all possible routing topologies of each
ECO net are derived based on Obstacle-Avoiding
Rectilinear Steiner Minimum Tree (OARSMT).

Second, the proposed ILP model is used to
optimally select the routing topology of each ECO
net.

Finally, the multi-source-multi-sink maze routing
model is facilitated to connect all ECO nets.
Obstacle-Avoiding Rectilinear Steiner
Minimum Tree (OARSMT)

Given a set T of n points, called terminals, and a
set O of m rectilinear obstacles in the plane, find
a set S of additional points, called Steiner points,
such that the length of a rectilinear minimum
spanning tree of T∪S, which avoids all obstacles
in O, is minimized.

Assign a corresponding parameter, ti, with initial
value 0 for each tile i. If the obtained OARSMT
pass through tile i, then increase ti by 1. Finally,
the tile with the maximum parameter value is
transformed into an pseudo-obstacle in later
OARSMT generation procedure.
Routing Topology Selection

Since the routing space have been occupied by a
great number of pre-routed nets and pre-placed
macros, only limited routing space can be
facilitated to perform ECO routing.

Besides, different routing orders and different
selected routing topologies which significantly
affect the routing quality should also be
considered.

The ILP model is adopted

Used to restrict only one routing topology of each
ECO net is chosen.

𝑥𝑖𝑗 is a Boolean variable which equals to 1 if the
𝑖
𝑗𝑡ℎ jth routing topology of ECO net 𝑁𝐸𝐶𝑂
is chosen.

Used to make sure all capacity constraints are
satisfied.

𝑘
𝑎𝑖𝑗
is a Boolean constant which equals to 1 if the
𝑖
𝑗𝑡ℎ routing topology of ECO net 𝑁𝐸𝐶𝑂
passes
through the tile boundary T𝐵𝑘 and 𝑐𝑘 is its
corresponding capacity.

Used to compute the number of changed masks
for the current routing solution.
 𝑙𝑖𝑗 denotes
the number of changed masks by
𝑖
choosing the 𝑗𝑡ℎ routing topology of ECO net 𝑁𝐸𝐶𝑂
.

I. TILE-BASED ROUTING GRAPH CONSTRUCTION

II. ECO ROUTING WITH MASK COST MINIMIZATION

III. NETWORK FLOW-BASED ECO ROUTING
REFINEMENT
NETWORK FLOW-BASED ECO ROUTING
REFINEMENT

In this section, an ECO routing refinement
approach is proposed to further reduce the
number of changed masks.

The key idea of ECO routing refinement is to
move each routing segment at the layer 𝐿𝑢𝑠𝑒𝑑
(i.e., the source layer) to the routing tracks at
the layer 𝐿𝑢𝑠𝑒𝑑 - 2 (i.e., the target layer).

To effectively reduce the number of changed
masks, an MCMF model is developed to
simultaneously distribute all target segments and
all rerouted segments to all available routing
tracks at the target layer.
EXPERIMENTAL RESULT
EXPERIMENTAL RESULT
EXPERIMENTAL RESULT
CONCLUSION

It is the first work to simultaneously optimize all
ECO nets to reduce the number of changed masks.