Large k-Gons in a 1.5D Terrain

Authors: Vahideh Keikha
Publication year: 2022
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Computing and Combinatorics: 28th International Conference, COCOON 2022 Proceedings
Projects: Structural properties of visibility in terrains and farthest color Voronoi diagrams
Bibliographic citation: KEIKHA, Vahideh. Large k-Gons in a 1.5D Terrain. In: ZHANG, Y., MIAO, D., MÖHRING, R., eds. Computing and Combinatorics: 28th International Conference, COCOON 2022 Proceedings. Cham: Springer, 2022, S. 49-60. Lecture Notes in Computer Science, 13595. ISBN 978-3-031-22104-0. ISSN 0302-9743. E-ISSN 1611-3349
Dostupné z: doi:10.1007/978-3-031-22105-7_5
DOI: 10.1007/978-3-031-22105-7_5
ID: 567939

Abstract

Given is a 1.5D terrain T, i.e., an x-monotone polygonal chain in R2. For a given 2 ≤ k≤ n, our objective is to approximate the largest area or perimeter convex object of exactly or at most k vertices inside T. For a constant k≥ 3, we design a near linear time FPTAS that approximates the largest convex polygons with at most k vertices, within a factor (1 - ϵ). For the case where k= 2, we discuss an O(n) time exact algorithm for computing the longest line segment in T, and for k= 3, we design an O(n2) time exact algorithm for computing the largest-perimeter triangle that lies within T.