Modeling API Rate Limits as Diophantine Inequalities
2025-06-30
This article explores a mathematical approach, specifically using Diophantine inequalities, to solve API rate limiting problems. The author uses a scenario with a 10-requests-per-hour limit and three retry attempts per task as an example, demonstrating how to transform the task scheduling problem into an integer feasibility problem. By analyzing the task retry pattern and time windows, the author establishes an inequality model and uses Go to write a program that determines whether a new task can be safely scheduled without exceeding the rate limit. The article also mentions optimizing the algorithm to reduce time complexity from O(n^2) to O(n*log(n)).