Robot Evacuation on a Line Assisted by a Bike
Abstract
:1. Introduction
1.1. Model and Notation
1.2. Related Work
1.3. Outline and Results of the Paper
2. Preliminaries
Algorithm 1: Zig-Zag Algorithm |
3. Evacuation in the Wireless (WiFi) Model
3.1. Opposite Direction with Max Speed
Algorithm 2: (OppDirectionWithMaxSpeedWiFi) |
3.2. Opposite Direction with Optimal Speed
Algorithm 3: (OppDirectionWithOptimalSpeedWiFi) |
3.3. Slower Imitates Faster
Algorithm 4: (SlowerImitateFasterWiFi) |
4. Evacuation in the Face-to-Face (F2F) Model
4.1. Slower Pursues Faster
Algorithm 5: (SlowerPursueFasterF2F) |
- Define to be the time needed by the biker to go to the exit from the point of intersection between the the biker and the hiker at then to return distance x to drop off the bike and subsequently go back to the exit. Thus can be defined as follows:
- Define to be the time needed by the hiker to go from the point of intersection between the hiker and the biker at to the exit while picking up the bike on its way. Thus can be defined as follows:
4.2. Slower Evacuation Close to Exit without Aid
Algorithm 6: (SlowerEvacuationCloseToExitWithoutAidF2F) |
4.3. Nearest Meeting to Exit
Algorithm 7: (EvacuatingWithBikeF2F) |
5. Lower Bounds
- If the hiker is located in the interval then the adversary places the exit at in which case by Theorem 7 the evacuation time will be at least .
- If the hiker is located in the interval then the adversary places the exit at in which case again by Theorem 7 the evacuation time will be at least .
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Algorithm | Theorem | Evacuation Time |
---|---|---|
Algorithm 2 (WiFi) | Theorem 1 | |
Algorithm 3 (WiFi) | Theorem 2 | |
Algorithm 4 (WiFi) | Theorem 3 | |
Algorithm 5 (F2F) | Theorem 4 | |
Algorithm 6 (F2F) | Theorem 5 | |
Algorithm 7 (F2F) | Theorem 6 | if |
if |
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Jawhar, K.; Kranakis, E. Robot Evacuation on a Line Assisted by a Bike. Information 2021, 12, 28. https://doi.org/10.3390/info12010028
Jawhar K, Kranakis E. Robot Evacuation on a Line Assisted by a Bike. Information. 2021; 12(1):28. https://doi.org/10.3390/info12010028
Chicago/Turabian StyleJawhar, Khaled, and Evangelos Kranakis. 2021. "Robot Evacuation on a Line Assisted by a Bike" Information 12, no. 1: 28. https://doi.org/10.3390/info12010028