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- James King, Erik Krohn
- SIAM J. Comput.
- 2010

A set <i>G</i> of points on a 1.5-dimensional terrain, also known as an <i>x</i>-monotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in <i>G</i>. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem… (More)

- Matt Gibson, Gaurav Kanade, Erik Krohn, Kasturi R. Varadarajan
- APPROX-RANDOM
- 2009

We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [2] and Mustafa and Ray [15]. Our key contribution is to show the existence of a planar graph that appropriately relates… (More)

- Erik Krohn, Matt Gibson, Gaurav Kanade, Kasturi R. Varadarajan
- JoCG
- 2014

We obtain a polynomial time approximation scheme for the 1.5D terrain guarding problem, improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [3] and Mustafa and Ray [18]. Our key contribution is to show the existence of a planar graph that appropriately… (More)

- Matt Gibson, Gaurav Kanade, Erik Krohn, Imran A. Pirwani, Kasturi R. Varadarajan
- SIAM J. Comput.
- 2008

Given a metric <i>d</i> defined on a set <i>V</i> of points (a metric space), we define the ball B(<i>v, r</i>) centered at <i>u</i> ∈ <i>V</i> and having radius <i>r</i> ≥ 0 to be the set {<i>q</i> ∈ <i>V/d(v, q)</i> ≤<i>r</i>}. In this work, we consider the problem of computing a minimum cost <i>k</i>-cover for a given set <i>P</i>… (More)

We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (see [14]). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the… (More)

- Matt Gibson, Gaurav Kanade, Erik Krohn, Imran A. Pirwani, Kasturi R. Varadarajan
- Algorithmica
- 2008

Given an n-point metric (P , d) and an integer k > 0, we consider the problem of covering P by k balls so as to minimize the sum of the radii of the balls. We present a randomized algorithm that runs in n O(log n·log) time and returns with high probability the optimal solution. Here, is the ratio between the maximum and minimum interpoint distances in the… (More)

- Erik Krohn, Bengt J. Nilsson
- CCCG
- 2012

A polygon P is x-monotone if any line orthogonal to the x-axis has a simply connected intersection with P. A set G of points inside P or on the boundary of P is said to guard the polygon if every point inside P or on the boundary of P is seen by a point in G. An interior guard can lie anywhere inside or on the boundary of the polygon. Using a reduction from… (More)

- Erik Krohn
- 2007

The terrain guarding problem and art gallery problem are two areas in computational geometry. Different versions of terrain guarding involve guarding a discrete set of points or a continuous set of points on a terrain. The art gallery problem has versions including guarding an entire polygon by a set of discrete points at the vertices or any point inside… (More)

- Matt Gibson, Erik Krohn, Qing Wang
- ISAAC
- 2015

- James King, Erik Krohn
- ArXiv
- 2009

A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if any point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem asks for a minimum… (More)