An Efficient Multi-Level Algorithm for 3D-IC TSV Assignment

Abstract

Through-silicon via (TSV) assignment problem is one of the key design challenges of 3-D IC which is crucial to the wire length and signal delay. In this work we formulate the 3-D IC TSV assignment as an Integer Minimum Cost Multi Commodity (IMCMC) problem on a IMCMC network, and propose a multi-level algorithm. It coarsens the IMCMC network level by level, applies a rough flow assignment on each level of coarsened graph, and generates only promising edges to reduce the IMCMC network size. Benefiting from the multi-level structure, we propose a mixed single and multi commodity flow method improve the TSV assignment solution quality. Moreover, given a TSV assignment, we propose an extended layer by layer algorithm to further optimize the TSV assignment. The experimental results demonstrate that our multi-level with mixed single and multi commodity flow algorithm achieves not only smaller wire length but also shorter runtime compared to other existing works.