Constructing Many Faces in Arrangements of Lines and Segments
Haitao Wang

TL;DR
This paper introduces improved algorithms for computing faces in arrangements of lines and segments, offering faster deterministic and randomized solutions, and addressing the query problem for efficient face location in planar arrangements.
Contribution
The paper presents new algorithms with better asymptotic performance for face computation in arrangements of lines and segments, including deterministic, randomized, and query-based methods.
Findings
Deterministic algorithm for lines with improved time complexity
Deterministic algorithm for segments with enhanced efficiency
Randomized algorithm for segments with expected faster performance
Abstract
We present new algorithms for computing many faces in arrangements of lines and segments. Given a set of lines (resp., segments) and a set of points in the plane, the problem is to compute the faces of the arrangements of that contain at least one point of . For the line case, we give a deterministic algorithm of time. This improves the previously best deterministic algorithm [Agarwal, 1990] by a factor of and improves the previously best randomized algorithm [Agarwal, Matou\v{s}ek, and Schwarzkopf, 1998] by a factor of in certain cases (e.g., when ). For the segment case, we present a deterministic algorithm of time, where and is the inverse Ackermann…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Point processes and geometric inequalities · Remote Sensing and LiDAR Applications
