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Electrowetting-on-dielectric (EWOD) chips have emerged as the most widely used actuators for digital microfluidic (DMF) systems. These devices enable the electrical manipulation of microfluidics with various advantages, such as low power consumption, flexibility, accuracy, and efficiency. In addressing the need for low-cost and practical fabrication, pin-count reduction has become a key problem to the large-scale integration of EWOD-chip designs. One of the major approaches, broadcast addressing, reduces the pin count by assigning a single control pin to multiple electrodes with mutually compatible control signals. Most previous studies utilize this addressing scheme by scheduling fluidic-level synthesis on pin-constrained chip arrays. However, the associated interconnect routing problem is still not provided in currently available DMF automations, and thus the broadcast-addressing scheme cannot be actually realized. In this paper, we present the first network-flow based pin-count aware routing algorithm for EWOD-chip designs with a broadcast electrode-addressing scheme. Our algorithm simultaneously takes pin-count reduction and wirelength minimization into consideration for higher integration and better design performance. Experimental results show the effectiveness and scalability of our algorithm on a set of real-life chip applications.