Guarding a 1.5D Terrain with Imprecise Viewpoints
Publication date
2025-07-18
Authors
Keikha, Vahideh
Löffler, Maarten
Saumell, Maria
Valtr, Pavel
Editors
Fernau, Henning
Zhu, Binhai
Advisors
Supervisors
Document Type
Part of book
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taverne
Abstract
Given an n-vertex 1.5D terrain T and a set of m edges of T, we study the problem of placing one viewpoint on each edge so that the total length of the visible portions of the terrain is maximized. We present an O(n+mlogm) time 12-approximation algorithm for the general problem, and polynomial-time algorithms for the cases m=1 and m=2. Additionally, we show that the problem of computing a point on T maximizing the visible portion of T can be solved in O(n3) time.
Keywords
1.5D terrain, Data imprecision, Multiple Viewpoints, Visibility, Taverne, Theoretical Computer Science, General Computer Science
Citation
Keikha, V, Löffler, M, Saumell, M & Valtr, P 2025, Guarding a 1.5D Terrain with Imprecise Viewpoints. in H Fernau & B Zhu (eds), Combinatorial Algorithms - 36th International Workshop, IWOCA 2025, Proceedings. Lecture Notes in Computer Science, vol. 15885 LNCS, Springer, pp. 3-16, 36th International Workshop on Combinatorial Algorithms, IWOCA 2025, Bozeman, United States, 21/07/25. https://doi.org/10.1007/978-3-031-98740-3_1, conference