Related papers: FPTAS for barrier covering problem with equal circ…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\max\{c^T x : Ax…
A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do…
We study the problem of stabbing rectilinear polygons, where we are given $n$ rectilinear polygons in the plane that we want to stab, i.e., we want to select horizontal line segments such that for each given rectilinear polygon there is a…
In the first part of this thesis, we consider an instance of Frechet distance problem in which the speed of traversal along each segment of the curves is restricted to be within a specfied range. This setting is more realistic than the…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…
This paper encompasses the mathematical derivations of the analytic and generalized formula and recurrence relations to find out the radii of n umber of circles inscribed or packed in the plane region bounded by circular arcs (including…
We study the problem of Covering Orthogonal Polygons with Rectangles. For polynomial-time algorithms, the best-known approximation factor is $O(\sqrt{\log n})$ when the input polygon may have holes [Kumar and Ramesh, STOC '99, SICOMP '03],…
We introduce the problem of finding a set $B$ of $k$ points in $[0,1]^n$ such that the expected cost of the cheapest point in $B$ that dominates a random point from $[0,1]^n$ is minimized. We study the case where the coordinates of the…
Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Fix $0 < \alpha < 1$. Let…
We investigate the problem of using mobile robots equipped with 2D range sensors to optimally guard perimeters or regions, i.e., 1D or 2D sets. Given such a set of arbitrary shape to be guarded, and $k$ mobile sensors where the $i$-th…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
We propose an $\widetilde{O}(n + 1/\eps)$-time FPTAS (Fully Polynomial-Time Approximation Scheme) for the classical Partition problem. This is the best possible (up to a polylogarithmic factor) assuming SETH (Strong Exponential Time…
Suppose we put an $\epsilon$-disk around each lattice point in the plane, and then we rotate this object around the origin for a set $\Theta$ of angles. When do we cover the whole plane, except for a neighborhood of the origin? This is the…
We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…
Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we…
The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments in sensor networks. A line segment ` is said…