Related papers: Largest Empty Circle Centered on a Query Line
The point placement problem is to determine the positions of a set of $n$ distinct points, P = {p1, p2, p3, ..., pn}, on a line uniquely, up to translation and reflection, from the fewest possible distance queries between pairs of points.…
Given $n$ points in a circular region $C$ in the plane, we study the problems of moving the $n$ points to its boundary to form a regular $n$-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the…
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…
A polygonal curve $P$ with $n$ vertices is $c$-packed, if the sum of the lengths of the parts of the edges of the curve that are inside any disk of radius $r$ is at most $cr$, for any $r>0$. Similarly, the concept of $c$-packedness can be…
We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fr\'echet distance. Given an $n$ vertex trajectory $P$ and an $m$ vertex query trajectory $Q$, we seek to report a vertex-aligned…
In the preprocessing framework one is given a set of regions that one is allowed to preprocess to create some auxiliary structure such that when a realization of these regions is given, consisting of one point per region, this auxiliary…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers.…
The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
For points $p_1,\ldots , p_n$ in the unit square $[0,1]^2$, an \emph{anchored rectangle packing} consists of interior-disjoint axis-aligned empty rectangles $r_1,\ldots , r_n\subseteq [0,1]^2$ such that point $p_i$ is a corner of the…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ…
This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container…
The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant…
Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…
We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case.…
This paper studies the \emph{$\varepsilon$-approximate range emptiness} problem, where the task is to represent a set $S$ of $n$ points from $\{0,\ldots,U-1\}$ and answer emptiness queries of the form "$[a ; b]\cap S \neq \emptyset$ ?" with…
The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < \alpha < 1$ and $n$ points such that $\alpha n$ of them are…
Circle graphs are intersection graphs of chords of a circle. In this paper, we present a new algorithm for the circle graph isomorphism problem running in time $O((n+m)\alpha(n+m))$ where $n$ is the number of vertices, $m$ is the number of…