Adjustable Coins
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability 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 specified cost, o...
Saved in:
| Published in | Recreational Mathematics Magazine Vol. 8; no. 15; pp. 27 - 39 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Sciendo
01.11.2021
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability 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 specified 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 different 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. |
|---|---|
| ISSN: | 2182-1976 2182-1976 |
| DOI: | 10.2478/rmm-2021-0009 |