Related papers: A linear time algorithm to cover and hit a set of …
In the paper "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", TCS Volume 769 (2019), pages 63--74, the LHIT problem is proposed as follows: For a given set of non-intersecting line…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let $\mathcal{P}$ be a set of $n$ weighted points in the plane. Let $D$ represent a planar object, such as a rectangle, or a disk. We…
In this paper, we consider the problems for covering multiple intervals on a line. Given a set $B$ of $m$ line segments (called "barriers") on a horizontal line $L$ and another set $S$ of $n$ horizontal line segments of the same length in…
In the Rectangle Stabbing problem, input is a set ${\cal R}$ of axis-parallel rectangles and a set ${\cal L}$ of axis parallel lines in the plane. The task is to find a minimum size set ${\cal L}^* \subseteq {\cal L}$ such that for every…
We consider an interval coverage problem. Given $n$ intervals of the same length on a line $L$ and a line segment $B$ on $L$, we want to move the intervals along $L$ such that every point of $B$ is covered by at least one interval and the…
Given a set $P$ of $n$ points and a set $S$ of $m$ weighted disks in the plane, the disk coverage problem asks for a subset of disks of minimum total weight that cover all points of $P$. The problem is NP-hard. In this paper, we consider a…
We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel…
Given a collection $L$ of line segments, we consider its arrangement and study the problem of covering all cells with line segments of $L$. That is, we want to find a minimum-size set $L'$ of line segments such that every cell in the…
Finding an optimal solution of signal traffic control durations is a computationally intensive task. It is typically O(T3) in time, and O(T2) in space, where T is the length of the control interval in discrete time steps. In this paper, we…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related {\em maximum path cover} problem, which asks for a collection of vertex disjoint paths that include the maximum number of…
Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles…
Given a rectangle $R$ with area $A$ and a set of areas $L=\{A_1,...,A_n\}$ with $\sum_{i=1}^n A_i = A$, we consider the problem of partitioning $R$ into $n$ sub-regions $R_1,...,R_n$ with areas $A_1,...,A_n$ in a way that the total…
Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…
Given a set $P$ of $n$ points and a set $S$ of $n$ weighted disks in the plane, the disk coverage problem is to compute a subset of disks of smallest total weight such that the union of the disks in the subset covers all points of $P$. The…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…