## 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 |