A new algorithm generates every possible arrangement of a list so fast that the time per arrangement is basically zero.
Ring-Cascade achieves sub-constant amortized time for permutation generation, a task that is usually limited by massive factorial scale. This leap in efficiency allows computers to cycle through billions of combinations at unprecedented speeds. The algorithm also provides a new way to solve the Superpermutation problem, a classic puzzle in combinatorial math. This breakthrough is a massive win for cryptography, logistics, and any field that deals with complex scheduling. It turns a slow mathematical process into a high-speed utility for modern computing.
Ring-Cascade: A Sub-constant Amortized Time Algorithm for High-Speed Permutation Generation
SSRN · 6553539
This paper presents the Ring-Cascade Permutation Algorithm, a high-efficiency generation framework for permutations that significantly reduces the operational overhead of classical combinatorial methods. By introducing a triple-segment memory mirroring topology, we demonstrate that the active decision logic can be structurally decoupled from the n! sequence scale. The framework reduces the total state-transition complexity to, while the majority of permutations are derived through deterministic