
Stabbing Rectangles by Line Segments  How Decomposition Reduces the ShallowCell Complexity
We initiate the study of the following natural geometric optimization pr...
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Parameterized Approximation Schemes for Independent Set of Rectangles and Geometric Knapsack
The area of parameterized approximation seeks to combine approximation a...
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The Maximum Exposure Problem
Given a set of points P and axisaligned rectangles ℛ in the plane, a po...
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Structured Discrete Shape Approximation: Theoretical Complexity and Practical Algorithm
We consider the problem of approximating a twodimensional shape contour...
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Faster Approximation Algorithms for Geometric Set Cover
We improve the running times of O(1)approximation algorithms for the se...
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Geometric Multicut
We study the following separation problem: Given a collection of colored...
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Promise Problems Meet Pseudodeterminism
The Acceptance Probability Estimation Problem (APEP) is to additively ap...
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A QPTAS for stabbing rectangles
We consider the following geometric optimization problem: Given n axisaligned rectangles in the plane, the goal is to find a set of horizontal segments of minimum total length such that each rectangle is stabbed. A segment stabs a rectangle if it intersects both its left and right edge. As such, this stabbing problem falls into the category of weighted geometric set cover problems for which techniques that improve upon the general Θ(log n)approximation guarantee have received a lot of attention in the literature. Chan at al. (2018) have shown that rectangle stabbing is NPhard and that it admits a constantfactor approximation algorithm based on Varadarajan's quasiuniform sampling method. In this work we make progress on rectangle stabbing on two fronts. First, we present a quasipolynomial time approximation scheme (QPTAS) for rectangle stabbing. Furthermore, we provide a simple 8approximation algorithm that avoids the framework of Varadarajan. This settles two open problems raised by Chan et al. (2018).
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