You are tasked with designing and implementing a randomized algorithm for [PROBLEM_DOMAIN], such as optimization, sampling, or cryptography. Your solution must balance efficiency and randomness while ensuring correctness. Outline the following: 1. The core idea behind the randomized approach for [SPECIFIC_USE_CASE]. 2. Key parameters to tune (e.g., probability thresholds, iteration counts) for [PERFORMANCE_METRIC]. 3. Pseudocode or a high-level implementation strategy, including how to handle edge cases like [FAILURE_SCENARIO]. 4. Expected time complexity and space complexity, justifying trade-offs. Provide a clear, step-by-step explanation suitable for both technical and non-technical stakeholders.