Practical Approximation Algorithms for Separable Packing Linear Programs

We describe fully polynomial time approximation schemes for generalized multicommodity flow problems arising in VLSI applications such as Global Routing via Buffer Blocks (GRBB). We extend Fleischer’s improvement [7] of Garg and Könemann [8] fully polynomial time approximation scheme for edge capacitated multicommodity flows to multiterminal multicommodity flows in graphs with capacities on vertices and subsets of vertices. In addition, our problem formulations observe upper bounds and parity constraints on the number of vertices on any source-to-sink path. Unlike previous works on the GRBB problem [5, 17], our algorithms can take into account (i) multiterminal nets, (ii) simultaneous buffered routing and compaction, and (iii) buffer libraries. Our method outperforms existing algorithms for the problem and has been validated on top-level layouts extracted from a recent high-end microprocessor design.