Papers by Pritha Banerjee
ACM Transactions on Embedded Computing Systems, 2009
Research in VLSI placement, an NP-hard problem, has branched in two different directions. The fir... more Research in VLSI placement, an NP-hard problem, has branched in two different directions. The first one employs iterative heuristics with many tunable parameters to produce near-optimal solution but without theoretical guarantee on its quality. The other one considers placement as graph embedding and designs approximation algorithms with provable bounds on the quality of the solution. In this paper, we aim at unifying the above two directions. First, we extend the existing approximation algorithms for graph embedding in 1D and 2D mesh to those for hypergraphs, which typically model circuits to be placed on a FPGA. We prove an O(d √ log n log log n) approximation bound for 1D and O(d log n log log n) approximation bound for the 2D mesh, where d is the maximum degree of hyperedges and n the number of vertices in the hypergraph. Next, we propose an efficient method based on linear arrangement of the CLBs, and the notion of space filling curves, for placing the configurable logic blocks (CLBs) of a netlist on island-style FPGAs with an approximation guarantee of O(d 4 √ log n √ k log log n). For the set of FPGA placement benchmarks, the running time is near-linear in the number of CLBs, thus allowing for scalability towards large circuits. We obtained on an average a 33× speedup with only 1.31× degradation in the quality of solution with respect to that produced by the popular FPGA tool VPR, thereby demonstrating the suitability of this very fast method for FPGA placement, with a provable performance guarantee.
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Papers by Pritha Banerjee