An Efficient Heuristic Algorithm for Linear Decomposition of Index Generation Functions

This paper proposes a heuristic algorithm for linear decomposition of index generation functions using a balanced decision tree. The proposed algorithm finds a good linear decomposition of an index generation function by recursively dividing a set of its function values into two subsets with balanced size. Since the proposed algorithm is fast and requires a small amount of memory, it is applicable even to large index generation functions that cannot be solved in a reasonable time by existing algorithms. This paper shows time and space complexities of the proposed algorithm, and experimental results using some large examples to show its efficiency. Keywords-Heuristic algorithm; balanced decision tree; linear decomposition; index generation functions; logic design.