Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time
In this paper, we introduce a linear program (LP)-based formulation of a rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by <inline-formula><math xmlns="http://www.w3.org/1998/M...
| Váldodahkkit: | , |
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| Materiálatiipa: | Artihkal |
| Giella: | English |
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MDPI AG
2022-01-01
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| Ráidu: | Algorithms |
| Fáttát: | |
| Liŋkkat: | https://www.mdpi.com/1999-4893/15/2/41 |
| _version_ | 1827657768638611456 |
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| author | Pierre Leone Nathan Cohen |
| author_facet | Pierre Leone Nathan Cohen |
| author_sort | Pierre Leone |
| collection | DOAJ |
| description | In this paper, we introduce a linear program (LP)-based formulation of a rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>v</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We observe that in this setting, a slow-moving player may have interest to remain still instead of moving. This shows that in some conditions the wait-for-mummy strategy is optimal. We observe as well that the strategies are completely different if the player that holds the marker is the fast or slow one. Interestingly, the marker is not useful when the player without marker moves slowly, i.e., the fast-moving player holds the marker. |
| first_indexed | 2024-03-09T22:49:37Z |
| format | Article |
| id | doaj.art-a63f9b51d83d4ef79c98ef6a39a8b8c8 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T22:49:37Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-a63f9b51d83d4ef79c98ef6a39a8b8c82023-11-23T18:24:03ZengMDPI AGAlgorithms1999-48932022-01-011524110.3390/a15020041Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen TimePierre Leone0Nathan Cohen1TCS-Sensor Lab, Centre Universitaire d’Informatique, Battelle Batiment A, Route de Drize 7, CH-1227 Carouge, SwitzerlandTCS-Sensor Lab, Centre Universitaire d’Informatique, Battelle Batiment A, Route de Drize 7, CH-1227 Carouge, SwitzerlandIn this paper, we introduce a linear program (LP)-based formulation of a rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>v</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We observe that in this setting, a slow-moving player may have interest to remain still instead of moving. This shows that in some conditions the wait-for-mummy strategy is optimal. We observe as well that the strategies are completely different if the player that holds the marker is the fast or slow one. Interestingly, the marker is not useful when the player without marker moves slowly, i.e., the fast-moving player holds the marker.https://www.mdpi.com/1999-4893/15/2/41asymmetric rendezvous on the linemarkersasymmetric speeds |
| spellingShingle | Pierre Leone Nathan Cohen Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time Algorithms asymmetric rendezvous on the line markers asymmetric speeds |
| title | Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time |
| title_full | Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time |
| title_fullStr | Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time |
| title_full_unstemmed | Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time |
| title_short | Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time |
| title_sort | rendezvous on the line with different speeds and markers that can be dropped at chosen time |
| topic | asymmetric rendezvous on the line markers asymmetric speeds |
| url | https://www.mdpi.com/1999-4893/15/2/41 |
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