Gaurav Kanade

An Approximation Scheme for Terrain Guarding

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 the local and global optimum.

Healthcare worker contact networks and the prevention of hospital-acquired infections.

We present a comprehensive approach to using electronic medical records (EMR) for constructing contact networks of healthcare workers in a hospital. This approach is applied at the University of Iowa Hospitals and Clinics (UIHC) – a 3.2 million square foot facility with 700 beds and about 8,000 healthcare workers – by obtaining 19.8 million EMR data points, spread over more than 21 months. We use these data to construct 9,000 different healthcare worker contact networks, which serve as proxies for patterns of actual healthcare worker contacts. Unlike earlier approaches, our methods are based on large-scale data and do not make any a priori assumptions about edges (contacts) between healthcare workers, degree distributions of healthcare workers, their assignment to wards, etc. Preliminary validation using data gathered from a 10-day long deployment of a wireless sensor network in the Medical Intensive Care Unit suggests that EMR logins can serve as realistic proxies for hospital-wide healthcare worker movement and contact patterns. Despite spatial and job-related constraints on healthcare worker movement and interactions, analysis reveals a strong structural similarity between the healthcare worker contact networks we generate and social networks that arise in other (e.g., online) settings. Furthermore, our analysis shows that disease can spread much more rapidly within the constructed contact networks as compared to random networks of similar size and density. Using the generated contact networks, we evaluate several alternate vaccination policies and conclude that a simple policy that vaccinates the most mobile healthcare workers first, is robust and quite effective relative to a random vaccination policy.

GUARDING TERRAINS VIA LOCAL SEARCH

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 (SoCG 2009) and Mustafa and Ray (DCG 2010). Our key contribution is to show the existence of a planar graph that appropriately relates the local and global optimum.

On Metric Clustering to Minimize the Sum of Radii

Given an n-point metric (P,d) and an integer k> 0, we consider the problem of covering Pby kballs so as to minimize the sum of the radii of the balls. We present a randomized algorithm that runs in nO(logn·logΔ)time and returns with high probability the optimal solution. Here, Δis the ratio between the maximum and minimum interpoint distances in the metric space. We also show that the problem is NP-hard, even in metrics induced by weighted planar graphs and in metrics of constant doubling dimension.

On isolating points using disks

In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not intercepted by some disk. We try to achieve this separation using a minimum number of a given set of unit disks. We show that a constant factor approximation to this problem can be found in polynomial time using a greedy algorithm. To the best of our knowledge we are the first to study this optimization problem.

On Clustering to Minimize the Sum of Radii

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> ⊆ <i>V</i> of <i>n</i> points, where <i>k</i> > 0 is some given integer which is also part of the input. For <i>k</i> ≥ 0, a <i>k</i>-cover for subset <i>Q</i> ⊆ <i>P</i> is a set of at most <i>k</i> balls, each centered at a point in <i>P</i>, whose union covers (contains) <i>Q.</i> The cost of a set <i>D</i> of balls, denoted cost(<i>D</i>), is the sum of the radii of those balls.

Topology construction for rural wireless mesh networks - a geometric approach

Wireless mesh networks based on the IEEE 802.11 technology have recently been proposed and studied as an approach to bridge the digital divide. Point-to-point links are established in the nodes of such networks using high gain directional antennas. Some nodes are directly linked to the wired internet, and the others link to these using a small number of hops. Minimization of system cost is an important objective in these networks, since generally the rural populations are low-paying. The dominant cost in this setting is that of constructing the antenna towers required to achieve Line-of-Sight connectivity. The cost of a tower depends upon its height, which in turn depends upon the length of its links and the physical obstacles along those links. We investigate the problem of selecting which links should be established such that all nodes are connected, while the cost of constructing the antenna towers is minimized. We formulate this as a geometric optimization problem, and develop an efficient approximation algorithm for the problem using techniques from facility location and geometric set cover. Our algorithm stands up well to experimental comparison with a computed lower bound and other approaches tried before. On the theoretical side, we are able to show that our algorithm guarantees a constant approximation factor... .