Balanced bipartitioning of a multi-weighted hypergraph for heterogeneous FPGAS

In this paper, we present a heuristic algorithm for bipartitioning a netlist of modules having m types of heterogeneous resources, as in modern FPGAs with configurable logic blocks (CLBs), Block RAMs and Multipliers (MULs). The desired min-cut bipartition has to satisfy m constraints arising from given balance ratios, one for each type of resource. The netlist is represented as a hypergraph, whose vertices correspond to the modules. Each vertex has a m-tuple weight vector, denoting the number of resource units of each type. Our proposed multi-constraint bipartitioner is based on dynamic programming, which employs a single-constraint bipartitioner. The upper bounds for mean deviation in combined balance ratio, and for the increment in cut-size are presented. Experimental results on a set of benchmarks show that on the average there is negligible deviation in cut-size for multi-constraint bipartitions from single-constraint bipartion, while satisfying the individual balance ratio constraints for each type of resource.