Simulated Bifurcation Algorithm for Combinatorial Optimization

The patent segments the combinatorial optimization problem into multiple sub-problems by dividing the set of all combinations into multiple subsets. Each subset is processed independently using parallel computation, transforming one large sequential problem into multiple smaller parallel tasks. This segmentation reduces the time complexity from exponential O(2^N) to approximately O(2^(N/k)) where k is the number of parallel segments, while maintaining solution accuracy through comprehensive search coverage.

The patent introduces a parallel computation dimension by utilizing multiple processing units (GPUs, FPGAs, or multi-core CPUs) to simultaneously evaluate different subsets of combinations. This dimensional transition from single-threaded sequential processing to multi-threaded parallel processing effectively reduces processing time while preserving the thoroughness of the combinatorial search through coordinated exploration of divided solution spaces.

The patent divides the enormous search space into multiple manageable subsets that can be processed in parallel. Each processing unit handles a specific subset with reduced computational complexity, while the coordination mechanism ensures comprehensive coverage of the entire search space. This segmentation transforms the intractable full-search problem into multiple tractable sub-problems that can be solved efficiently with available computational resources.

The patent merges the results from multiple parallel processing units to form the final optimized solution. By combining the partial results from different subsets through a coordination mechanism, the system achieves thorough exploration of the entire search space while distributing the computational burden across multiple units, thereby reducing individual device complexity requirements.

The patent segments the combinatorial optimization task into independent sub-tasks that can be executed in parallel across multiple processing units. This segmentation enables linear speedup where processing time is reduced approximately by a factor of k (number of parallel units), while each individual unit maintains relatively simple processing logic compared to solving the full problem sequentially.

The patent employs universal processing units (such as GPUs or FPGAs) that can handle multiple subsets of the search space through reconfigurable or highly parallel architectures. These multi-functional units can dynamically adapt to process different subsets, reducing the need for dedicated hardware for each subset and thereby managing system complexity while maintaining high parallel processing productivity.