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- Matt Gibson, Kasturi R. Varadarajan
- Discrete & Computational Geometry
- 2011

- Matt Gibson, Imran A. Pirwani
- ESA
- 2010

We consider the problem of finding a lowest cost dominating set in a given disk graph containing n disks. The problem has been extensively studied on subclasses of disk graphs, yet the best known approximation for disk graphs has remained O(log n) – a bound that is asymptotically no better than the general case. We improve the status quo in two ways: for… (More)

- Jeannine Coburn, Matt Gibson, +5 authors Jennifer H . Elisseeff
- Smart structures and systems
- 2011

The native extracellular matrix (ECM) consists of an integrated fibrous protein network and proteoglycan-based ground (hydrogel) substance. We designed a novel electrospinning technique to engineer a three dimensional fiber-hydrogel composite that mimics the native ECM structure, is injectable, and has practical macroscale dimensions for clinically relevant… (More)

- Matt Gibson, Imran A. Pirwani
- ArXiv
- 2010

We consider the problem of finding a lowest cost dominating set in a given disk graph containing n disks. The problem has been extensively studied on subclasses of disk graphs, yet the best known approximation for disk graphs has remained O(log n) – a bound that is asymptotically no better than the general case. We improve the status quo in two ways: for… (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)

- 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
- 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 Δ) time and returns with high probability the optimal solution. Here, Δ is the ratio between the maximum and minimum interpoint distances in the… (More)

- Matt Gibson, Dongfeng Han, Milan Sonka, Xiaodong Wu
- ISAAC
- 2011

We consider an optimization version of the image segmentation problem, in which we are given a grid graph with weights on the grid cells. We are interested in finding the maximum weight subgraph such that the subgraph can be decomposed into two ”star-shaped” images. We show that this problem can be reduced to the problem of finding a maximum-weight closed… (More)

- Matt Gibson, Kasturi R. Varadarajan
- 2009 50th Annual IEEE Symposium on Foundations of…
- 2009

We show that a k-fold covering using translates of an arbitrary convex polygon can be decomposed into Omega(k) covers (using an efficient algorithm). We generalize this result to obtain a constant factor approximation to the sensor cover problem where the ranges of the sensors are translates of a given convex polygon. The crucial ingredient in this… (More)