English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Given a planar subdivision whose coordinates are integers bounded by U ≤ 2w [U less than or equal to 2 superscript w], we present a linear-space data structure that can answer point-location queries in O(min{lg n/ lg lg n, sq rt lg U/ lg lgU}) [O(min {lg n / lg lg n, square root of lg U/lg lg U})] time on the unit-cost random access machine (RAM) with word size w. This is the first result to beat the standard Θ [theta](lg n) bound for infinite precision models. As a consequence, we obtain the first o(n lg n) (randomized) algorithms for many fundamental problems in computational geometry for arbitrary integer input on the word RAM, including: constructing the convex hull of a three-dimensional (3D) point set, computing the Voronoi diagram or the Euclidean minimum spanning tree of a planar point set, triangulating a polygon with holes, and finding intersections among a set of line segments. Higher-dimensional extensions and applications are also discussed. Though computational geometry with bounded precision input has been investigated for a long time, improvements have been limited largely to problems of an orthogonal flavor. Our results surpass this long-standing limitation, answering, for example, a question of Willard (SODA'92).Natural Sciences and Engineering Research Council of Canad

Transdichotomous Results in Computational Geometry, I: Point Location in Sublogarithmic Time