Visibility Queries in Simple Polygons
Sujoy Bhore, Chih-Hung Liu, Anurag Murty Naredla, Yakov Nekrich, Eunjin Oh, Andr\'e van Renssen, Frank Staals, Haitao Wang, and Jie Xue

TL;DR
This paper introduces new data structures for visibility queries in simple polygons, balancing space and query time, and proposes a novel polygon decomposition method.
Contribution
It presents several improved data structures for visibility queries with different space-time trade-offs and introduces a new polygon decomposition technique.
Findings
Achieves $O( log n + k)$ query time with $O(n^{2+psilon})$ space.
Improves query time to $O( log n log log n + k)$ with $O(n^2)$ space.
Provides a new polygon decomposition method of independent interest.
Abstract
Given a simple polygon with vertices, we consider the problem of constructing a data structure for visibility queries: for any query point , compute the visibility polygon of in . To obtain query time, where is the size of the visibility polygon of , the previous best result requires space. In this paper, we propose a new data structure that uses space, for any , while achieving the same query time. If only space is available, the best known result provides query time. We improve this to time. When restricted to space, the only previously known approach, aside from the -time algorithm that computes the visibility polygon without preprocessing, is an -space data structure that supports -time queries. We…
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