Abstract
In this paper we consider a scenario where there are several algorithms
for solving a given problem. Each algorithm is associated with a proba-
bility of success and a cost, and there is also a penalty for failing to solve
the problem. The user may run one algorithm at a time for the specied
cost, or give up and pay the penalty. The probability of success may be
implied by randomization in the algorithm, or by assuming a probability
distribution on the input space, which lead to dierent variants of the
problem. The goal is to minimize the expected cost of the process under
the assumption that the algorithms are independent. We study several
variants of this problem, and present possible solution strategies and a
hardness result.
for solving a given problem. Each algorithm is associated with a proba-
bility of success and a cost, and there is also a penalty for failing to solve
the problem. The user may run one algorithm at a time for the specied
cost, or give up and pay the penalty. The probability of success may be
implied by randomization in the algorithm, or by assuming a probability
distribution on the input space, which lead to dierent variants of the
problem. The goal is to minimize the expected cost of the process under
the assumption that the algorithms are independent. We study several
variants of this problem, and present possible solution strategies and a
hardness result.
| Original language | American English |
|---|---|
| Pages (from-to) | 27-39 |
| Number of pages | 13 |
| Journal | recreational mathematics magazine |
| Volume | 8 |
| Issue number | 15 |
| State | Published - 2021 |