Online Maximum k-Coverage

We study an online model for the maximum k-vertex-coverage problem, where given a graph G = (V,E) and an integer k, we ask for a subset A ⊆ V, such that |A | = k and the number of edges covered by A is maximized. In our model, at each step i, a new vertex vi is revealed, and we have to decide whether we will keep it or discard it. At any time of the process, only k vertices can be kept in memory; if at some point the current solution already contains k vertices, any inclusion of any new vertex in the solution must entail the irremediable deletion of one vertex of the current solution (a vertex not kept when revealed is irremediably deleted). We propose algorithms for several natural classes of graphs (mainly regular and bipartite), improving on an easy 1/2-competitive ratio. We next settle a set-version of the problem, called maximum k-(set)-coverage problem. For this problem we present an algorithm that improves upon former results for the same model for small and moderate values of k

Better Streaming Algorithms for the Maximum Coverage Problem

We study the classic NP-Hard problem of finding the maximum k-set coverage in the data stream model: given a set system of m sets that are subsets of a universe {1,...,n}, find the k sets that cover the most number of distinct elements. The problem can be approximated up to a factor 1-1/e in polynomial time. In the streaming-set model, the sets and their elements are revealed online. The main goal of our work is to design algorithms, with approximation guarantees as close as possible to 1-1/e, that use sublinear space o(mn). Our main results are: 1) Two (1-1/e-epsilon) approximation algorithms: One uses O(1/epsilon) passes and O(k/epsilon^2 polylog(m,n)) space whereas the other uses only a single pass but O(m/epsilon^2 polylog(m,n)) space. 2) We show that any approximation factor better than (1-(1-1/k)^k) in constant passes require space that is linear in m for constant k even if the algorithm is allowed unbounded processing time. We also demonstrate a single-pass, (1-epsilon) approximation algorithm using O(m/epsilon^2 min(k,1/epsilon) polylog(m,n)) space. We also study the maximum k-vertex coverage problem in the dynamic graph stream model. In this model, the stream consists of edge insertions and deletions of a graph on N vertices. The goal is to find k vertices that cover the most number of distinct edges. We show that any constant approximation in constant passes requires space that is linear in N for constant k whereas O(N/epsilon^2 polylog(m,n)) space is sufficient for a (1-epsilon) approximation and arbitrary k in a single pass. For regular graphs, we show that O(k/epsilon^3 polylog(m,n)) space is sufficient for a (1-epsilon) approximation in a single pass. We generalize this to a K-epsilon approximation when the ratio between the minimum and maximum degree is bounded below by K

Maternity Care and Consumer-Driven Health Plans

Compares out-of-pocket costs of maternity care under consumer-driven health plans (CDHP) to a traditional health insurance plan. Explores related factors including prenatal care coverage and unpredictability of costs for delivery and hospital stays

Underlay Drone Cell for Temporary Events: Impact of Drone Height and Aerial Channel Environments

Providing seamless connection to a large number of devices is one of the biggest challenges for the Internet of Things (IoT) networks. Using a drone as an aerial base station (ABS) to provide coverage to devices or users on ground is envisaged as a promising solution for IoT networks. In this paper, we consider a communication network with an underlay ABS to provide coverage for a temporary event, such as a sporting event or a concert in a stadium. Using stochastic geometry, we propose a general analytical framework to compute the uplink and downlink coverage probabilities for both the aerial and the terrestrial cellular system. Our framework is valid for any aerial channel model for which the probabilistic functions of line-of-sight (LOS) and non-line-of-sight (NLOS) links are specified. The accuracy of the analytical results is verified by Monte Carlo simulations considering two commonly adopted aerial channel models. Our results show the non-trivial impact of the different aerial channel environments (i.e., suburban, urban, dense urban and high-rise urban) on the uplink and downlink coverage probabilities and provide design guidelines for best ABS deployment height.Comment: This work is accepted to appear in IEEE Internet of Things Journal Special Issue on UAV over IoT. Copyright may be transferred without notice, after which this version may no longer be accessible. arXiv admin note: text overlap with arXiv:1801.0594

On the effectiveness of run-time checks

Run-time checks are often assumed to be a cost-effective way of improving the dependability of software components, by checking required properties of their outputs and flagging an output as incorrect if it fails the check. However, evaluating how effective they are going to be in a future application is difficult, since the effectiveness of a check depends on the unknown faults of the program to which it is applied. A programming contest, providing thousands of programs written to the same specifications, gives us the opportunity to systematically test run-time checks to observe statistics of their effects on actual programs. In these examples, run-time checks turn out to be most effective for unreliable programs. For more reliable programs, the benefit is relatively low as compared to the gain that can be achieved by other (more expensive) measures, most notably multiple-version diversity