NCKU CSIE EDALAB

Tsung-Wei Huang, Chun-Hsien Lin, and Tsung-Yi Hohttp://eda.csie.ncku.edu.tw

Department of Computer Science and Information EngineeringNational Cheng Kung University

Tainan, Taiwan

ACM/IEEE International Conference on Computer Aided Design

NCKU CSIE EDALAB

Outline

IntroductionIntroduction

Problem FormulationProblem Formulation

AlgorithmsAlgorithms

Experimental ResultsExperimental Results

ConclusionConclusion

NCKU CSIE EDALAB

Digital MicroFluidic Biochip (DMFB)

Side view

Top view

Droplet

Bottom plate

Top plate

Ground electrode

Control electrodes (cells)

Hydrophobic insulation

Droplet Spacing

High voltage to generate an electric field

The schematic view of a biochip (Duke Univ.)

Reservoir/Dispensing port

Droplets

Control electrodes

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Routing Constraints

․ Fluidic constraint¾ For the correctness of droplet transportation¾ No unexpected mixing among droplets of different nets¾ Static and dynamic fluidic constraints

․ Timing constraint¾ Maximum transportation time of droplets

Static fluidic constraint

Minimum spacing

Dynamic fluidic constraint

X

YT

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Contamination problem

Disjoint routes

Routing with the wash droplet

S1

S2

T1

T2

2D microfluidic array

M

d1

d2

d1

d2

d1

d2

Dispensing port

Reservoir port

W

Routing Constraints

․ Contamination problem

d1

d2

W

(1) separately

(2) simultaneously

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Outline

IntroductionIntroduction

Problem FormulationProblem Formulation

AlgorithmsAlgorithms

Experimental ResultsExperimental Results

ConclusionConclusion

NCKU CSIE EDALAB

Droplet Routing on Digital Microfluidic Biochips (DMFBs)

․ Input: A netlist of n droplets D = {d1, d2,…, dn}, the locations of blockages, and the timing constraint Tmax

․ Objective: Route all droplets from their source cells to their target cells while minimizing the number of used cells and execution time for better fault tolerance and reliability

․ Constraint: Fluidic, timing and contamination constraints should be satisfied.

2D microfluidic arrayDroplets

Target

• Fluidic constraint

• Timing constraint

Minimum spacing

Static fluidic constraint Dynamic fluidic constraint

• Contamination constraint

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Related Work

Droplet Routing Algorithm Droplet routing in the synthesis of digital microfluidic biochips

[Su et al, DATE’06] Modeling and controlling parallel tasks in droplet based microfluidic systems

[K. F. B hringer, TCAD’06] A network-flow based routing algorithm for digital microfluidic biochips

[Yuh et al, ICCAD’07] Integrated droplet routing in the synthesis of microfluidic biochips

[T. Xu and K. Chakrabarty, DAC’07] A high-performance droplet routing algorithm for digital microfluidic biochips

[Cho and Pan, ISPD’08]

Contamination-Aware Droplet Routing Algorithm Cross-contamination avoidance for droplet routing in digital microfluidic

biochips [Y. Zhao and K. Chakrabarty, DATE’09] Disjoint routes Wash operation insertion strategy

o :

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DATE’09

Total execution time for bioassay

Subproblem SP1

Subproblem SP2

Subproblem SPn

Subproblem SPn-1

Execution time of bioassay (time cycle)

Bio

log

ical

rea

ctio

n o

rder

…

I(1,2) I(2,3) I(n-1,n)

SP2

W2

SP1

W1

W1,2

W2,3

Wn-1,n

SPn

Wn

SPn-1

Wn-1

…

Sequencing relationship

Wash operation between subproblemsSubproblem of bioassayWash operation within one subproblem

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Ours

Total execution time for bioassay

Subproblem SP1

Subproblem SP2

Subproblem SPn

Subproblem SPn-1

Execution time of bioassay (time cycle)

Bio

log

ical

rea

ctio

n o

rder

I(1,2)

SP1

W1

W1,2

…

I(2,3) I(n-1,n)

SP2

W2

W2,3

Wn-1,n

SPn

Wn

SPn-1

Wn-1

…

Sequencing relationship

Wash operation between subproblemsSubproblem of bioassayWash operation within one subproblem

SP1

W1,2

W1

SP2

W2,3

W2

SPn-1

Wn-1,n

Wn-1

Reduced timeTotal execution time for bioassay

NCKU CSIE EDALAB

Outline

IntroductionIntroduction

Problem FormulationProblem Formulation

AlgorithmsAlgorithms

Experimental ResultsExperimental Results

ConclusionConclusion

Preprocessing Stage

Intra-Contamination Aware Routing Stage

Inter-Contamination AwareRouting Stage

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Preprocessing Stage

․ Preferred routing tracks construction¾ Reduce the design complexity for droplet routing¾ Minimize the used cells for better fault-tolerance¾ Increase the routability by concession control

․ Routing priority calculation¾ Routing-resource-based equation that considers the interference

between droplets inside the routing region globally¾ Increase the routability for droplet routing

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Preprocessing Stage

S1

S2

T1

T3

T2

d3

d1

d2

․ Example

Moving vector analysis

Routing tracks construction

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Preprocessing Stage

S1

S2

T1

T3

T2

Res1eq=((16+0)-(2+3))/16 = 11/16

Res2eq=((15+3)-(0))/18 = 1

Res3eq=((18+10)-(2+3))/28 =23/28

Route d2 to the A-cell of T2 by min-cost path

d1

S3

Concession Control

d2

d3

Res3eq=((18+10)-(2+6))/28 =20/28

Res1eq=((16+0)-(2))/16 = 14/16

․ Example

Moving vector analysis

Routing tracks construction

Routing priority calculation

Minimum cost path

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Intra-Contamination Aware Routing Stage

․ Routing path modification by k-shortest path¾ Minimize the intra-contaminated spots while modifying the

routing path slightly

․ Routing compaction by dynamic programming¾ Minimize the completion time for bioassays (a series 2D routing

path to 3D routing path)

․ Minimum cost circulation flow technique¾ Schedule the wash operation for wash droplets¾ Solve the intra-contaminated spots optimally under our flow

construction

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Routing Path Modification by k-shortest Path

․ A k-shortest based algorithm¾ Modify the original routing path slightly¾ Minimize the contaminated spots

S1 T1

S2

T2

S3

T3

Contaminated spots:

6 -> 6 -> 2

Original routing path

Select a highly contaminated path

Find the first shortest path

Find the second shortest path

Contamination spots Routing path Si Source location Ti Target location

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Routing Compaction by Dynamic Programming

․ Major goals:¾ Transform the 2D routing into 3D routing considering the timing

issue and maintain the original routing path¾ Estimate an initial timing slot of each contaminated spot

․ Optimal substructure¾ Optimally solution for a pair of droplets

¾ Find the solution by dynamic programming incrementally

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․ Illustration of dynamic programming¾ Decode the 2D routing path into the1D moving string (u, d, l, r)

․ Incremental compaction strategy

P1 P2 P3 P4 Pn-1 Pn

compactioncompactioncompaction

…

compactioncompaction

Routing Compaction by Dynamic Programming

S1 T1

S2

T2

MS1: rrrrrrMS2: dddddrrrr

d d d d d r r r r

0 1 2 3 4 5 6 7 8 9

r X X X X 4 5 6 7 8 9

r X X X X X 5 6 7 8 9

r X X X X X X 6 7 8 9

r X X X X X X X 7 8 9

r X X X X X X X X 8 9

r X X X X X X X X X 9

Compaction

d1

d2

d2

d2

d2

d2

d2 d2 d2 d2 d2

d1 d1 d1 d1 d1 d1

Used time = 9

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Minimum Cost Circulation Flow Technique

․ Introduction to minimum cost circulation (MCC) problem¾ A generalization of network flow problems¾ Constraints:

Bounded constraint:

- each flow arc has a lower bound and a upper bound

Conservation constraint:

- the net flow of each node is zero

¾ Objective: Minimize the cost:

ijijij uxl

ff Eijji

Ejiij xx

),(),(

fEji

ijij xCz),(

NCKU CSIE EDALAB

Minimum Cost Circulation Flow Technique

․ Circulation flow formulation¾ Schedule an optimal solution for correct wash operation ¾ Four main phases of formulation

․ Two basic assignments¾ Node capacity assignment¾ Edge cost assignment

․ Two construction rules¾ Timing-based transitive topology¾ Connection strategy between phases

wash droplets

wastereservoircontaminated

spots

dropletsource

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Minimum Cost Circulation Flow Technique

․ Assignment 1: Node capacity assignment¾ Guarantee that the contaminated spot should be cleaned by

the wash droplets Node split

․ Assignment 2: Edge cost assignment¾ Minimize the used cells and routing time of wash droplets¾ The same routing cost model between two points

node split into input node and output node

VIO

node v

assign the 3-tuple (l, u, c) of this arc

)0,,1(

Rc

shoulderillegallegalvv cccRCostji

)()( ),(

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Minimum Cost Circulation Flow Technique

․ Construction rule 1: Timing-based transitive topology¾ Timing-based topology

The timing slot of each contaminated spot can be estimate by dynamic programming

Connect a early contaminated spot to a later one by the 3-tuple

¾ Transitive closure Allows the multiple wash droplets to perform the wash

operation, while satisfying the timing-based topology For any triple contaminated spot (vi, vk, vj), if there are

edges connect and , a transitive edge also connects by assigning the

))(,,0( , ji vvRCost

),( kin

iout vv ),( j

inkout vv

),( jin

iout vv ))(,,0( , ji vv

RCost

NCKU CSIE EDALAB

Minimum Cost Circulation Flow Technique

․ Illustration

VIO

VIO

VIO

VIO

…

Contaminated spots

Assignment 1

Assignment 2

)0,,1(

)0,,1(

)0,,1(

)0,,1(

Timing-based topology

1̂t

2̂t

3̂t

nt̂

ntttt ˆˆˆˆ321

Transitive closure

Transitive edge

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Minimum Cost Circulation Flow Technique

․ Construction rule 2: connection between phases¾ Four major phases in the MCC formulation

)0,4,1(

W3

W1

W2

W4

L = 0U = 1C = 0

L = 0U = 1C = min-cost path

L = 0U = ∞ C = min-cost path

Source

Sink

...

...I O

I O

I O

I O

. ..

Source Wash droplets Contaminated spots Waste reservoir

NCKU CSIE EDALAB

Minimum Cost Circulation Flow Technique

․ Theorem 1: There exists a feasible solution under the two basic assignments and two flow construction rules

¾ Proof The construction enhances at least one flow from the sink

back to the source, meaning that one flow from the source to the wash droplet set. There also exists one possible path to travel all the contaminated node set (topology sorted order).

S TW

Flow lower bound=1

C1

C2

Cn

Topology sorted order …

At least one wash droplet

Clean the contaminated spots

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Minimum Cost Circulation Flow Technique

․ Theorem 2: Under the proposed flow construction, we can adopt the MCC algorithm to schedule correct and optimal wash operations

¾ Proof Theorem 1 shows there is a feasible solution, that is, the

contaminated spots are correctly cleaned by the wash droplets.

The MCC algorithm will obtain a feasible flow with minimum cost that represents the optimal scheduling of wash operations.

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Inter-Contamination Aware routing Stage

․ Look-Ahead routing scheme¾ Contaminated spots also occur between subproblems¾ Predicting the inter-contaminations for the next subproblem

and clean the intra- and inter-contaminations simultaneously to reduce the completion time

Inter-contamination Intra-contamination

si si+1 si and si+1

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Inter-Contamination Aware routing Stage

․ Travelling salesman problem optimization¾ Utilize the wash droplets while minimize the total used cells

and completion time¾ Clean the set of non-washed look-ahead contaminated spots in

the bounding box of node vi and vj

Vi

Vj

(vi, vj) is the edge of flow graphConsider the bounding box

Inter- and Intra- contaminated spots

Construction rule 1

TSP optimization

Inter-contaminated spots

Intra-contaminated spots

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Outline

IntroductionIntroduction

Problem FormulationProblem Formulation

AlgorithmsAlgorithms

Experimental ResultsExperimental Results

ConclusionConclusion

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Experimental Settings

․ Implement our algorithm in C++ language on a 2 GHz 64-bit Linux machine with 8GB memory

․ Comparison¾ Disjoint-route algorithm [Y. Zhao and K. Chakrabarty, DATE’09]

․ Tested on three benchmark suites¾ Benchmark [Su and Chakrabarty, DAC’05]

Circuit Size #Sub #Net #Dmax #W

in-vitro_1 16 x 16 11 28 5 4

in-vitro_2 14 x 14 15 35 6 4

protein_1 21 x 21 64 181 6 4

protein_2 13 x 13 78 178 6 4

Size: Size of the microfluidic array

#Sub: Number of subproblems

#Net: Total input nets

#Dmax: Maximum number of droplets with one subproblem

#W: Number of wash droplets

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BioassayOurs (non k-SP) Ours (k-SP)

#Cintra #UC Texe CPU #Cintra #UC Texe CPU

in-vitro_1 53 388 225 0.18 21 351 193 0.58

in-vitro_2 27 291 217 0.13 5 281 191 0.39

protein_1 138 2418 1592 1.47 82 2213 1394 2.58

protein_2 106 1453 1280 0.71 61 1362 1108 1.49

Total 324 4550 3314 2.49 169 4207 2886 5.04

#Cintra: The number of intra-contaminations

CPU: The CPU time (sec)Texe: The execution time for the bioassays

BioassayContaminations Ours (non look-ahead) Ours (look-ahead)

#Cintra #Cinter #Cintra #UC Texe CPU #UC Texe CPU

in-vitro_1 21 19 21 446 227 0.32 351 193 0.58

in-vitro_2 5 8 5 267 210 0.24 281 191 0.39

protein_1 82 190 82 2493 1569 2.11 2213 1394 2.58

protein_2 61 141 61 1498 1172 0.47 1362 1108 1.49

Total 169 358 169 4704 3178 3.14 4207 2886 5.04

#UC: The number of used cells for routing

#Cintra: The number of intra-contaminations

#Ciinter: The number of inter-contaminations

CPU: The CPU time (sec)

#UC: The number of used cells for routing

Texe: The execution time for the bioassays

7.54%12.91%

10.57%

9.19%

47.84%

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CircuitDisjoint route (Y. Zhao and K. Chakrabarty) Ours (k-SP + look-ahead)

#CS #UC Texe CPU #CS #UC Texe CPU

in-vitro_1 4 621 268 0.06 21 351 193 0.58

in-vitro_2 0 423 224 0.03 5 281 191 0.39

protein_1 18 3215 1508 0.23 82 2213 1394 2.58

protein_2 11 1574 1287 0.14 61 1362 1108 1.49

Total 33 5833 3287 0.46 169 4207 2886 5.04

#Cintra: The number of intra-contaminations

CPU: The CPU time (sec)

#UC: The number of used cells for routing

Texe: The execution time for the bioassays

27.88%

12.20%

NCKU CSIE EDALAB

Outline

IntroductionIntroduction

Problem FormulationProblem Formulation

AlgorithmsAlgorithms

Experimental ResultsExperimental Results

ConclusionConclusion

NCKU CSIE EDALAB

Conclusion

․ We proposed a contamination aware droplet router for DMFBs

․ We can optimally solve the wash droplets routing for the intra-contamination problem

․ Furthermore, the experimental results shown that our algorithm can achieve better timing result (Texe) and fault tolerance (#UC) compared with the best known results

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