A framework for the analysis and design of algorithms for a class of VLSI-CAD optimization problems

A simple mathematical framework, called cluster-cover, is established for several VLSI optimisation problems including logic minimization, constrained encoding, multi-layer topological planar routing, application timing assignment for delay-fault testing, and minimization of monitoring logic for BIST enhancement. Two paradigms, prime covering and greedy peeling, are presented for developing both exact and heuristic algorithms. The paradigms capture generally applicable ingredients from previously developed algorithms for individual applications. This makes it possible to re-use established techniques in new problems, and provide new insights into existing problems. The paradigms are simple enough to be amenable to theoretical analysis. Bounds on the performance of greedy peeling are derived; these bounds are applicable to many published heuristics which previously could be evaluated only by benchmarks.