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A provably tight delay-driven concurrently congestion mitigating global routing algorithm
Samanta, R.,Erzin, A.I.,Raha, S.,Shamardin, Y.V.,Takhonov, I.I.,Zalyubovskiy, V.V. Elsevier [etc.] 2015 Applied mathematics and computation Vol.255 No.-
Routing is a very important step in VLSI physical design. A set of nets are routed under delay and resource constraints in multi-net global routing. In this paper a delay-driven congestion-aware global routing algorithm is developed, which is a heuristic based method to solve a multi-objective NP-hard optimization problem. The proposed delay-driven Steiner tree construction method is of O(n<SUP>2</SUP>logn) complexity, where n is the number of terminal points and it provides n-approximation solution of the critical time minimization problem for a certain class of grid graphs. The existing timing-driven method (Hu and Sapatnekar, 2002) has a complexity O(n<SUP>4</SUP>) and is implemented on nets with small number of sinks. Next we propose a FPTAS Gradient algorithm for minimizing the total overflow. This is a concurrent approach considering all the nets simultaneously contrary to the existing approaches of sequential rip-up and reroute. The algorithms are implemented on ISPD98 derived benchmarks and the drastic reduction of overflow is observed.