Contiguous Boundary Guarding
| Autor: | Biniaz, Ahmad, Maheshwari, Anil, Mitchell, Joseph S. B., Odak, Saeed, Polishchuk, Valentin, Shermer, Thomas |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the problem of guarding the boundary of a simple polygon with a minimum number of guards such that each guard covers a contiguous portion of the boundary. First, we present a simple greedy algorithm for this problem that returns a guard set of size at most OPT + 1, where OPT is the number of guards in an optimal solution. Then, we present a polynomial-time exact algorithm. While the algorithm is not complicated, its correctness proof is rather involved. This result is interesting in the sense that guarding problems are typically NP-hard and, in particular, it is NP-hard to minimize the number of guards to see the boundary of a simple polygon, without the contiguous boundary guarding constraint. From the combinatorial point of view, we show that any $n$-vertex polygon can be guarded by at most $\lfloor \frac{n-2}{2}\rfloor$ guards. This bound is tight because there are polygons that require this many guards. Comment: 16 pages of body text; 3 pages of references; 13 figures |
| Databáze: | arXiv |
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