Overflow-Aware Via Placement for Dense Die-to-Die Connections in Advanced Package Routing

With the rapid development of advanced packaging technology of heterogeneous integration, via placement in die-todie (D2D) package routing becomes a challenging problem. The complex via-related design rules and limited routing resources due to staggered vias make conventional via placement strategies no longer applicable. Poor via placement can significantly degrade the routability and quality of the final routing result. To tackle this challenge, we first model a quadratically constrained quadratic programming (QCQP) formulation for this complex via placement problem. We further propose acceleration techniques to reduce the problem size while maintaining the solution quality. Experimental results show that our accelerated QCQP-based algorithm effectively reduces the runtime of the original QCQP formulation and can produce overflow-free routing solutions for benchmarks derived from industrial design in $\mathrm{O}\left(\mathrm{n}^{1.53}\right)$ empirical time.