garantiproblem

The garantiproblem is a term used in theoretical computer science to denote a class or type of problem in which guarantees about the solution are central. At its core, a garantiproblem asks not only for a correct solution but for formal assurances about the solution’s properties, such as optimal value, runtime, or resource usage, across all valid instances of a given size.

In formal terms, given an instance I of problem P, an algorithm A is said to guarantee a property G if, whenever A is applied to I, it produces a result S such that G(I, S) holds, within predefined resource bounds. Guarantees may be exact (S is optimal), approximate (S is within a factor alpha of the optimum), deterministic (the guarantee holds with probability 1), or probabilistic (the guarantee holds with probability p). Common axes for guarantees are correctness, approximation ratio, and time/space complexity.

Variants include worst-case guarantees (guarantees hold for all inputs of size n), average-case guarantees (hold on average over a distribution of inputs), and online guarantees (solutions adapt as data arrives). The concept is often used to compare algorithms, design robust systems, and analyze the limits of computation.

Related notions include guarantee theory, competitive analysis, and approximation theory. While not a standard term in mainstream literature, garantiproblem serves as a helpful shorthand in discussions of what it means to "guarantee" a solution under specified constraints.