DAC Presentation kit

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Placement of Digital Microfluidic Biochips Using
the T-tree Formulation

• Ping-Hung Yuh1, Chia-Lin Yang1, and Yao-Wen Chang2

1 Dept. of Computer Science Information
Engineering 2 Graduate Institute of Electronics
Engineering and Dept. of Electrical
Engineering National Taiwan University, Taiwan
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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Digital Microfluidic Biochips

• Perform laboratory procedures based on liquid
  particles (droplets)
• The two main components
• Reconfigurable devices (electrodes)
• Droplets can move freely on the reconfigurable
  device
• Non-reconfigurable devices (detectors and
  reservoirs)
• Only one functionality

Optical detector
Droplets
Storage
Electrodes
The schematic view of a biochip (Duke Univ.)
Mixing two droplets
Reservoirs/Dispensing ports
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Digital Microfluidic Biochips (contd)
Mix
Storage
Dilution
Time 14
Time 45
Mix
Mix
Dilution
Dilution
a
b
Mix
c
Task graph
Time 57
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Placement Problem of Biochips

• Inputs
• Sequencing graph
• Microfluidic module library
• Design specification
• Fixed architecture (ex 5x5-array) and maximum
  assay completion time (ex 400 sec)
• Limited number of non-reconfigurable devices
• Output the schedule and placement of tasks

Microfluidic Module Library
A sequencing graph
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Previous Work

• Architecture-level synthesis (scheduling and
  binding)
• Deng et al, TCAD01
• Architecture-level model and ILP-based method
• Su and Chakrabarty, ICCAD04
• Sequencing graph model and two heuristics
• Physical placement
• Su and Chakrabarty, DATE05
• Simulated annealing based algorithm with given
  scheduled tasks
• Unified synthesis and placement
• Su and Chakrabarty, DAC05
• Parallel recombinative simulated annealing
• List scheduling and greedy placement method

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Our Contribution

• Formulate the execution of a bioassay as a 3D
  floorplan
• Apply a tree-based representation (T-tree) to
  solve the floorplanning/placement problem

Mix
Storage
Mix
Dilute
Storage
Mix
Time t2
Mix
Mix
Dilute
Mix
Time t1
Time t3
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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Bioassay Execution to 3D floorplan

• Model each task and storage as a 3D box
• Model the execution of a bioassay as a 3D
  floorplan
• Biochip placement problem to 3D temporal
  floorplanning problem

Dilute
Storage
Mix
Time t2
Storage
Mix
Mix
Mix
Mix
Dilute
Mix
Time t1
Time t3
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Review of T-tree

• A 3-ary tree representation for
  temporalfloorplanning/placement problem

Mix b
Dilute c
Storagess
Storagess
Mix a
Mix a
Mix b
Dilute c
A 3D compacted floorlpan
The corresponding T-tree
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Review of T-tree (contd)

• The T-tree keeps the geometric relation as
  follows
• Left child adjacent in the T direction
• Middle child in the Y direction with the same
  t-coordinate
• Right child in the X direction with the same t-
  and y-coordinates

Mix b
Dilute c
Ti duration of i
Storage s
Storages
Mix a
Mix a
Mix b
Dilute c
ti starting time of i
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Modeling Tasks in a T-tree

• Model each task as a node in a T-tree

f
Dispense
c
e
a
b
d
The corresponding T-tree
A sequencing graph
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Modeling Storages

• Model each storage as a node in a T-tree
• Each edge in a sequencing graph represents a
  storage

f
Dispense
c
e
s2
s1
Storage
a
b
s2
s1
s4
s3
d
s5
s3
s4
s5
The corresponding T-tree
A sequencing graph
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Modeling Storages (contd)

• The storage constraint the duration of one
  storage covers the time gap between two
  data-dependent tasks
• Insert a storage node in one of the feasible
  locations in a T-tree
• Ensure that ts tb Tb

t
c
s
Tb
b
feasible location
b
tatbTb
tb
tdteta
a
s
d
c
e
Example of feasible locations
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Modeling the Design Specification

• The fixed-cube constraint
• Model the fixed architecture and max. completion
  time as a 3D cube
• A feasible floorplan must be within this 3D cube
• The resource constraint
• of non-reconfigurable tasks is limited at any
  time
• Add the virtual edges in the sequencing graph

Virtual edge
Max. completion time
A feasible floorplan
Fixed architecture
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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Floorplanning Algorithm

• Based on simulated annealing (SA)
• The modified SA flow
• Detect the violation of the storage constraints
• Delete unused storages in a T-tree for packing
  efficiency

Perturbation
Storage Constraint
Feasibility Detection Tree Reconstruction
Data Dependency
Number of storagesAdjustment
Packing
Termination?
No
Yes
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Floorplanning Algorithm (contd)

• Cost function
• Volume
• of storages
• Penalty term for fixed-cube constraint

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Two Methods for Fixed-cube Constraint

• Guide the tree perturbation based on cube
  violation probability pw, ph, and pt
• pw k/n, where k is the of floorplans whose
  width exceeds the 3D cube in the last n
  iterations
• If pw is large, increase the probability of
  placing tasks along the Y or T direction
• Add the excessive length into the cost function

An infeasible floorplan
Max. completion time
Excessive length
Fixed architecture
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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Experimental Settings

• Implemented our algorithm in C language on a
  1.2 GHz SUN Blade-2000 machine with 8GB memory
• Implemented the algorithm of Su and
  Chakrabarty, DAC05 on the same machine
• Tested two bioassays
• Colorimetric protein assay from Su and
  Chakrabarty, DAC05
• Multiplexed in-virto diagnostics from Su and
  Chakrabarty, ICCAD04
• Assigned three different design specifications
  (fixed-cube constraints) to each bioassay

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Experimental Result
Bioassay DesignSpec. Su et al, DAC05 Su et al, DAC05 T-tree T-tree
Bioassay DesignSpec. Volume CPU time(seconds) Volume CPU time(seconds)
ProteinSu et al, DAC05 10x10x400 9x10x400 300 10x10x270 89
ProteinSu et al, DAC05 10x10x360 10x10x342 225 10x10x282 119
ProteinSu et al, DAC05 11x11x320 8x13x269 208 11x11x238 66
Avg. 1.16 2.67 1.0 1.0
In vitro Su et al, ICCAD04 10x10x100 9x11x99 64 9x8x66 6
In vitro Su et al, ICCAD04 8x8x120 9x9x130 104 8x7x68 12
In vitro Su et al, ICCAD04 7x7x140 9x10x105 92 6x7x89 15
Avg. 2.42 7.88 1.0 1.0
volume area assay completion time
Result that cannot satisfy the fixed-cube
constraint
T-tree based algorithm is more efficient and
effective
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Resulting Placement of the Protein Bioassay
Volume 10x10x270 (10x10x400 fixed-cube
constraint)
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Outline

• Introduction
• T-tree Based Placement Formulation
• Floorplanning Algorithm
• Experimental Result
• Conclusion

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Conclusion

• Formulated the placement problem of biochips as
  the temporal floorplanning problem
• First work to apply a topological representation
  to the placement problem of biochips
• Demonstrated the effectiveness and efficiency of
  our algorithm
• Future work
• Consider fault and defect tolerance during
  floorplanning

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Thank you for your attention
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Q A
r91089_at_csie.ntu.edu.tw
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Question 1

• Q Why choose the T-tree representation over
  other 3D representations (3D-subTCG, ST,
  3D-slicing tree) ?
• A Three reasons
• 1. T-tree models the compacted floorplan, thus it
  has the advantage of volume optimization
• 2. T-tree is more efficient for large-scale
  circuits than 3D-subTCG, ST
• 3. T-tree is more effective in handling the
  storages
• T-tree can determine the of storages and
  duration of each storage before packing with only
  O(n) time
• 3D-subTCG and ST needs O(n2) time before packing
• 3D-slicing tree cannot obtain this information
  before packing
• It is difficult for 3D-slicing tree to satisfy
  the storage constraint

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Question 2

• Q Why add the of storages in the cost
  function?
• A Two reasons
• 1. Generally, the smaller of storages, the more
  compact 3D floorplan we can have
• 2. Release the volume occupied by storages for
  reconfigurable task to use

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Question 3

• Q Why your algorithm is better than previous
  work?
• A There are two reasons
• 1. T-tree is better in volume optimization than
  previous greedy placement method
• 2. Smoother optimization process by minimizing
  volume instead of area plus completion time