Practical Approximation Algorithms for Separable Packing Linear Programs Feodor F. Dragan 1 , Andrew B. Kahng 2 , Ion I. M˘ andoiu 3 , Sudhakar Muddu 4 , and Alexander Zelikovsky 5 1 Department of Computer Science, Kent State University, Kent, OH 44242 dragan@cs.kent.edu 2 Departments of Computer Science and Engineering, and of Electrical and Computer Engineering, UC San Diego, La Jolla, CA 92093-0114 abk@cs.ucsd.edu 3 Department of Computer Science, UC Los Angeles, Los Angeles, CA 90095-1596 mandoiu@cc.gatech.edu 4 Sanera Systems, Inc., Santa Clara, CA muddu@sanera.net 5 Department of Computer Science, Georgia State University, Atlanta, GA 30303 alexz@cs.gsu.edu Abstract. We describe fully polynomial time approximation schemes for gen- eralized multicommodity flow problems arising in VLSI applications such as Global Routing via Buffer Blocks (GRBB). We extend Fleischer’s improvement [7] of Garg and K¨ onemann [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 prob- lem 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) simultane- ous buffered routing and compaction, and (iii) buffer libraries. Our method out- performs existing algorithms for the problem and has been validated on top-level layouts extracted from a recent high-end microprocessor design. 1 Introduction In this paper, we address the problem of how to perform buffering of global nets given an existing buffer block plan. We give integer linear program (ILP) formulations of the basic Global Routing via Buffer Blocks (GRBB) problem and its extensions to (i) multiterminal nets, (ii) simultaneous buffered routing and compaction, and (iii) buffer libraries. The fractional relaxations of these ILP’s are separable packing LP’s (SP LP) which are multiterminal multicommodity flows in graphs with capacities on vertices and subsets of vertices. The main contribution of this paper is a practical algorithm for the GRBB problem and its extensions based on a fully polynomial time approximation scheme (FPTAS) This work was partially supported by Cadence Design Systems, Inc., the MARCO Gigascale Silicon Research Center and NSF Grant CCR-9988331.