A Network-Flow Based Algorithm for Digital Microfluidic Biochip Routing Ping-Hung Yuh, Chia-Lin Yang, and Yao-Wen Chang Department of CSIE, NTU 18th VLSI Design/CAD Symposium, Taiwan, 2007

Outline Introduction Droplet Routing Problem Biochip Routing Algorithm Global Routing – Network based Detailed Routing – Negotiation based Experimental Results Conclusions

Introduction Electrowetting on Dielectric (EWOD) 絕緣層電潤濕現象 The digital microfluidic biochips are based on the manipulation of droplets in a 2D array The basic operations (e.g., mix, dilute, etc.) can be performed anywhere in the 2D array Electrodes can be re-programmed

Droplet Routing A droplet can move to an adjacent cell when the corresponding electrode is activated The droplet routing problem is to route all droplets From a source pin to a target pin From a source pin to a waste reservoir From a reservoir/dispensing port to a target pin

Droplet Routing (cont.) Sequentially route each 2D plane to determine the routing path and schedule of each droplet Fluidic constraint To avoid the unexpected mixing of two droplets of different nets during their transportation Timing constraint The maximum allowed transportation time of a droplet

Fluidic Constraints Static fluidic constraint The minimum spacing between two droplets is one cell Dynamic fluidic constraint No other droplets can stay in the 3D cube, when dp is located at cell c at time tp t = tp t = tp + 1 t = tp - 1

Timing Constraint The maximum allowed transportation time of a droplet d from its source s to target c: Tmax Earliest reaching time: minT(c, d) = md(c, s) Latest time of staying at c: maxT(c, d) = Tmax - md(c, s) c is available to d at time t if maxT ≥ minT Idle interval: [minT(c, d), maxT(c, d)] The timing interval that d can stay at c Violation interval: [minT(c, d) - 1, maxT(c, d) + 1] No other droplets can be scheduled in violation interval at c or the neighboring cells of c

Droplet Routing Problem of One 2D Plane Given Netlist of nets, where each net is a 2-pin net (one droplet) or a 3-pin net (two droplets) Location of pins and obstacles Timing constraint Objective Route all droplets from their source pins to target pins Minimize the number of cells for routing Constraint Both the fluidic and the timing contraints are satisfied

Biochip Routing Algorithm

Net Criticality A net n is said to be critical if n has few possible solutions (routing paths and schedules) due to timing constraint The routing solution of n will be affected by other nets u(c, n, t) is 1 if c is available to net n at time t

Global Routing Determine a rough routing path for each droplet Decompose into a set of subproblems by selecting a set of independent nets that do not interfere with each other Two nets are said to be independent nets if Their bounding boxes do not overlap, or All cells in the overlapping area are violation-free cells One cell such that the idle interval of d1 overlaps with violation interval of d2  Not violation-free cell Construct a conflict graph for net selection

Network-Flow Based Routing Algorithm Use min-cost max-flow (MCNF) algorithm to solve each subproblem Divide a biochip into a set of global cells gc Each global cell contains 3x3 basic cells A node vpa in the flow graph represents At least one cell c in gcp is available to da and c is in the bounding box of net a

Network-Flow Based Routing Algorithm (cont.) Each node has its capacity Kp – UGp Kp is the capacity of a global cell p Total time of each droplet staying at each cell in gcp UGp is the number of droplets that currently uses gcp Each node has its cost Φ(vpa) |N’|: # input nets, snp: # input nets that can use gcp Encourage multiple droplets to share the same global cell Encourage two nets in N’ to share the same global cell

Handling 3-pin Nets Route the droplet d1 with a longer Manhattan distance first Then route d2 to one of the global cells, common mixing nodes, that are used by d1 Common Mixing Nodes

Detailed Routing Ref.: “Pathfinder: a negotiation-based perfrormance-driven router for fpgas,” L. McMurchie and C. Ebeling, in FPGA,1995 Route and schedule each droplet in the decreasing order of their criticality Determine the arrival and departure times of each droplet on each cell To find the minimum cost routing tree RTa for each droplet on net a

Negotiation Based Algorithm Construct a routing graph A unique node vp for each cell cp vp and vq are connected via a directed edge if droplets can move from cp to cq The node vp is associated with its cost UC(vp) is 0 if cp is used by at least one droplet The F term is to guide to satisfy the fluidic constraint If the fluidic constraint is violated in many previous iterations, F will be large. The router tends not to use vp at time t to route droplets

Experimental Results Compared with [5] Smaller total number of cells used for routing (237 vs. 267) Less CPU time (0.03 sec vs. 0.15 sec)

Conclusions First network-flow based routing algorithm for digital microfluidic biochip routing Compared with recent routing works, the algorithm can achieve better solution quality with less CPU time