KD-LBA: a Kernighan Lin-driven logarithmic barrier approach to solve the many-to-many assignment problem and its application in CPU/FPGA scheduling

The many-to-many assignment problem (M- MAP), and the CPU/FPGA scheduling problem are two correlated issues in the field of combinatorial optimization. The framework for Kernighan Lin-driven logarithmic barrier approach (KD-LBA) is made to solve the many-to-many assignment problem. KD-LBA is a deterministic technique, which initiates to achieve the globally optimal solutions for MMAP using logarithmic barrier function-based gradient descent technique. Then, the obtained solution is optimized further using the Kernighan Lin-based local search method. Successive Kernighan Lin-driven logarithmic barrier approach (Successive KD-LBA) is also proposed to sort the issue of scheduling in a CPU/FPGA heterogeneous system. It solves the CPU/ FPGA scheduling problem by transforming it into an MMAP. KD-LBA outperforms the state-of-art methods in terms of convergence speed for MMAPs with a group size greater than 40. Successive KD-LBA presents novel scheduling solutions for the CPU/FPGA scheduling problem as compared to the existing works, regarding average makespan and computation time.