Linear Search with Probabilistic Detection and Variable Speeds
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909610486530048 |
|---|---|
| author | Coleman, Jared Morales-Ponce, Oscar |
| author_facet | Coleman, Jared Morales-Ponce, Oscar |
| contents | We present results on new variants of the famous linear search (or cow-path) problem that involves an agent searching for a target with unknown position on the infinite line. We consider the variant where the agent can move either at speed $1$ or at a slower speed $v \in [0, 1)$. When traveling at the slower speed $v$, the agent is guaranteed to detect the target upon passing through its location. When traveling at speed $1$, however, the agent, upon passing through the target's location, detects it with probability $p \in [0, 1]$. We present algorithms and provide upper bounds for the competitive ratios for three cases separately: when $p=0$, $v=0$, and when $p,v \in (0,1)$. We also prove that the provided algorithm for the $p=0$ case is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Search with Probabilistic Detection and Variable Speeds Coleman, Jared Morales-Ponce, Oscar Discrete Mathematics We present results on new variants of the famous linear search (or cow-path) problem that involves an agent searching for a target with unknown position on the infinite line. We consider the variant where the agent can move either at speed $1$ or at a slower speed $v \in [0, 1)$. When traveling at the slower speed $v$, the agent is guaranteed to detect the target upon passing through its location. When traveling at speed $1$, however, the agent, upon passing through the target's location, detects it with probability $p \in [0, 1]$. We present algorithms and provide upper bounds for the competitive ratios for three cases separately: when $p=0$, $v=0$, and when $p,v \in (0,1)$. We also prove that the provided algorithm for the $p=0$ case is optimal. |
| title | Linear Search with Probabilistic Detection and Variable Speeds |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2505.09429 |