相关论文: A (7/2)-Approximation Algorithm for Guarding Ortho…
Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S…
Bandyapadhyay et al. introduced the generalized minimum-membership geometric set cover (GMMGSC) problem [SoCG, 2023], which is defined as follows. We are given two sets $P$ and $P'$ of points in $\mathbb{R}^{2}$, $n=\max(|P|, |P'|)$, and a…
The minimum sum-of-squares clustering problem (MSSC) consists of partitioning $n$ observations into $k$ clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose…
We study the Maximum Independent Set of Rectangles (MISR) problem, where we are given a set of axis-parallel rectangles in the plane and the goal is to select a subset of non-overlapping rectangles of maximum cardinality. In a recent…
We present a complete classification of minimal problems for generic arrangements of points and lines in space observed partially by three calibrated perspective cameras when each line is incident to at most one point. This is a large class…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path.…
The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given $n$ points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and…
A sliding k-transmitter in an orthogonal polygon P is a mobile guard that travels back and forth along an orthogonal line segment s inside P. It can see a point p in P if the perpendicular from p onto s intersects the boundary of P at most…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
Given a simple polygon $\mathcal{P}$ on $n$ vertices, two points $x,y$ in $\mathcal{P}$ are said to be visible to each other if the line segment between $x$ and $y$ is contained in $\mathcal{P}$. The Point Guard Art Gallery problem asks for…
We show the following problems are in $\textsf{P}$: 1. The contiguous art gallery problem -- a variation of the art gallery problem where each guard can protect a contiguous interval along the boundary of a simple polygon. This was posed at…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
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…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
In this paper, we present the first constant-approximation algorithm for {\em budgeted sweep coverage problem} (BSC). The BSC involves designing routes for a number of mobile sensors (a.k.a. robots) to periodically collect information as…
We consider the classical Minimum Crossing Number problem: given an $n$-vertex graph $G$, compute a drawing of $G$ in the plane, while minimizing the number of crossings between the images of its edges. This is a fundamental and extensively…
We consider the problem of tracking $n$ targets in the plane using $2n$ cameras. We can use two cameras to estimate the location of a target. We are then interested in forming $n$ camera pairs where each camera belongs to exactly one pair,…