相关论文: Efficient Range Reporting of Convex Hull

We present self-adjusting data structures for answering point location queries in convex and connected subdivisions. Let $n$ be the number of vertices in a convex or connected subdivision. Our structures use $O(n)$ space. For any convex…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our…

We present a new fully dynamic algorithm for maintaining convex hulls under insertions and deletions while supporting geometric queries. Our approach combines the logarithmic method with a deletion-only convex hull data structure, achieving…

Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in…

It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…

We consider the following problem: Preprocess a set $\mathcal{S}$ of $n$ axis-parallel boxes in $\mathbb{R}^d$ so that given a query of an axis-parallel box in $\mathbb{R}^d$, the pairs of boxes of $\mathcal{S}$ whose intersection…

In this paper, we investigate the homothetic point enclosure problem: given a set $S$ of $n$ triangles with sides parallel to three fixed directions, find a data structure for $S$ that can report all the triangles of $S$ that contain a…

$\def\DD{{{\bf \delta}}}\def\CH{{\mathop{\mathrm{ConvexHull}}}}\newcommand{\LL}{{\cal {L}}} \newcommand{\ZZ}{\mathbb{Z}} $ Given a convex body $C$ in the plane, its discrete hull is $C^0 = \CH( C \cap \LL )$, where $\LL = \ZZ \times \ZZ$ is…

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of $n$ vertices and $h$ holes. We introduce a \emph{graph of oriented distances} to encode the distance between…

The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for…

Let $P$ be a simple polygon with $n$ vertices, and let $A$ be a set of $m$ points or line segments inside $P$. We develop data structures that can efficiently count the number of objects from $A$ that are visible to a query point or a query…

We present a novel 2D convex hull peeling algorithm for outlier detection, which repeatedly removes the point on the hull that decreases the hull's area the most. To find k outliers among n points, one simply peels k points. The algorithm…

We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results.…

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group…

We consider the problem of preprocessing $N$ points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of…

We present new iterative algorithms for solving a square linear system $Ax=b$ in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time approximation scheme for testing if the convex hull of a finite…

Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of $n$ points in strictly convex normed planes can be constructed in $O(n \log n)$ time. In addition, we confirm that,…

We study the problem of constructing a data structure that can store a two-dimensional polygonal curve $P$, such that for any query segment $\overline{ab}$ one can efficiently compute the Fr\'{e}chet distance between $P$ and…

We present two cache-oblivious sorting-based convex hull algorithms in the Binary Forking Model. The first is an algorithm for a presorted set of points which achieves $O(n)$ work, $O(\log n)$ span, and $O(n/B)$ serial cache complexity,…