You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Let @math be a point in a polygonal domain @math of @math holes and @math vertices. We consider a quickest visibility query problem. Given a query point @math in @math , the goal is to find a shortest path in @math to move from @math to see @math as quickly as possible. Previously, (SoCG 2015) built a data structure of size @math that can answer each query in @math time, where @math is the inverse Ackermann function and @math is the size of the visibility polygon of @math in @math (and @math can be @math in the worst case). In this paper, we present a new data structure of size @math that can answer each query in @math time. Our result improves the previous work when @math is relatively small. In particular, if @math is a constant, then our result even matches the best result for the simple polygon case (i.e., @math ), which is optimal. As a by-product, we also have a new algorithm for a shortest-path-to-segment query problem. Given a query line segment @math in @math , the query seeks a shortest path from @math to all points of @math . Previously, gave a data structure of size @math that can answer each query in @math time, and another data structure of size @math with @math query time. We present a data structure of size @math with query time @math , which also favors small values of @math and is optimal when @math .

Cited Abstract(s):
[1]: We show how to preprocess a polygonal domain with a fixed starting point s in order to answer efficiently the following queries: Given a point q, how should one move from s in order to see q as soon as possible? This query resembles the well-known shortest-path-to-a-point query, except that the latter asks for the fastest way to reach q, instead of seeing it. Our solution methods include a data structure for a different generalization of shortest-path-to-a-point queries, which may be of independent interest: to report efficiently a shortest path from s to a query segment in the domain.
For the quickest visibility queries, [1] also built a quickest visibility map'' of @math size in @math time, which can answer each query in @math time. In addition, [1] gave a conditional lower bound on the problem by showing that the 3SUM problem on @math numbers can be solved in @math time, where @math is the preprocessing time and @math is the query time. Therefore, a data structure of @math preprocessing time and @math query time would lead to an @math time algorithm for 3SUM.