Rapid growth in capacity makes flow-based microfluidic biochips a promising candidate for biochemical analysis because they can integrate more complex functions. However, as the number of components grows, the total length of flow channels between components must increase exponentially. Recent empirical studies show that long flow channels are vulnerable due to blocking and leakage defects. Thus, it is desirable to minimize the total length of flow channels for robustness. Also, for timing-sensitive biochemical assays, increase in the longest length of flow channel will delay the assay completion time and lead to variation of fluid, thereby affecting the correctness of outcome. The increasing number of components, including the pre-placed components, on the chip makes the flow channel routing problem even more complicated. In this paper, we propose an efficient obstacleavoiding rectilinear Steiner minimum tree algorithm to deal with flow channel routing problem in flow-based microfluidic biochips. Based on the concept of Kruskal algorithm and formulating the considerations as a bi-criteria function, our algorithm is capable of simultaneously minimizing the total length and the longest length of flow channel.

We consider the multi-layer obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem and propose a reduction to transform a multi-layer instance into a 3D instance. Based on the reduction we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.

Given a set of pin-vertices, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects all the pin-vertices possibly through Steiner points using vertical and horizontal segments with the minimal wirelength and without intersecting any obstacle. To deal with multiple routing layers and preferred routing orientations, we consider the multilayer obstacle-avoiding rectilinear Steiner minimal tree (ML-OARSMT) problem and the obstacle-avoiding preferred direction Steiner tree (OAPD-ST) problem. First, we prove that the multilayer case is theoretically different from the 2D one, and propose a reduction to transform a multilayer instance into a 3D instance. Based on the reduction, we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics, for the ML-OARSMT problem and the OAPD-ST problem. Furthermore, we develop an advanced Steiner point selection to avoid inferior Steiner points and to improve the solution quality. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.

Rapid growth in capacity makes flow-based microfluidic biochips a promising candidate for biochemical analysis because they can integrate more complex functions. However, as the number of components grows, the total length of flow channels between components must increase exponentially. Recent empirical studies show that long flow channels are vulnerable due to blocking and leakage defects. Thus, it is desirable to minimize the total length of flow channels for robustness. Also, for timing-sensitive biochemical assays, increase in the longest length of flow channel will delay the assay completion time and lead to variation of fluid, thereby affecting the correctness of outcome. The increasing number of components, including the pre-placed components, on the chip makes the flow channel routing problem even more complicated. In this paper, we propose an efficient obstacleavoiding rectilinear Steiner minimum tree algorithm to deal with flow channel routing problem in flow-based microfluidic biochips. Based on the concept of Kruskal algorithm and formulating the considerations as a bi-criteria function, our algorithm is capable of simultaneously minimizing the total length and the longest length of flow channel.

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