461 research outputs found

    On the complexity of barrier resilience for fat regions and bounded ply

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    In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so that two fixed points can be connected without crossing any region. In this paper, we show that the problem is NP-hard when the collection only contains fat regions with bounded ply Âż (even when they are axis-aligned rectangles of aspect ratio ). We also show that the problem is fixed-parameter tractable (FPT) for unit disks and for similarly-sized Ăź-fat regions with bounded ply Âż and pairwise boundary intersections. We then use our FPT algorithm to construct an -approximation algorithm that runs in time, where .Peer ReviewedPostprint (author's final draft

    The Maximum Exposure Problem

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    Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points

    How to Navigate Through Obstacles?

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    Given a set of obstacles and two points in the plane, is there a path between the two points that does not cross more than k different obstacles? This is a fundamental problem that has undergone a tremendous amount of work by researchers in various areas, including computational geometry, graph theory, wireless computing, and motion planning. It is known to be NP-hard, even when the obstacles are very simple geometric shapes (e.g., unit-length line segments). The problem can be formulated and generalized into the following graph problem: Given a planar graph G whose vertices are colored by color sets, two designated vertices s, t in V(G), and k in N, is there an s-t path in G that uses at most k colors? If each obstacle is connected, the resulting graph satisfies the color-connectivity property, namely that each color induces a connected subgraph. We study the complexity and design algorithms for the above graph problem with an eye on its geometric applications. We prove a set of hardness results, among which a result showing that the color-connectivity property is crucial for any hope for fixed-parameter tractable (FPT) algorithms, as without it, the problem is W[SAT]-hard parameterized by k. Previous results only implied that the problem is W[2]-hard. A corollary of this result is that, unless W[2] = FPT, the problem cannot be approximated in FPT time to within a factor that is a function of k. By describing a generic plane embedding of the graph instances, we show that our hardness results translate to the geometric instances of the problem. We then focus on graphs satisfying the color-connectivity property. By exploiting the planarity of the graph and the connectivity of the colors, we develop topological results that allow us to prove that, for any vertex v, there exists a set of paths whose cardinality is upper bounded by a function of k, that "represents" the valid s-t paths containing subsets of colors from v. We employ these structural results to design an FPT algorithm for the problem parameterized by both k and the treewidth of the graph, and extend this result further to obtain an FPT algorithm for the parameterization by both k and the length of the path. The latter result generalizes and explains previous FPT results for various obstacle shapes, such as unit disks and fat regions

    Revisiting the Minimum Constraint Removal Problem in Mobile Robotics

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    The minimum constraint removal problem seeks to find the minimum number of constraints, i.e., obstacles, that need to be removed to connect a start to a goal location with a collision-free path. This problem is NP-hard and has been studied in robotics, wireless sensing, and computational geometry. This work contributes to the existing literature by presenting and discussing two results. The first result shows that the minimum constraint removal is NP-hard for simply connected obstacles where each obstacle intersects a constant number of other obstacles. The second result demonstrates that for nn simply connected obstacles in the plane, instances of the minimum constraint removal problem with minimum removable obstacles lower than (n+1)/3(n+1)/3 can be solved in polynomial time. This result is also empirically validated using several instances of randomly sampled axis-parallel rectangles.Comment: Accepted for presentation at the 18th international conference on Intelligent Autonomous System 202

    Minimum Shared-Power Edge Cut

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    We introduce a problem called the Minimum Shared-Power Edge Cut (MSPEC). The input to the problem is an undirected edge-weighted graph with distinguished vertices s and t, and the goal is to find an s-t cut by assigning "powers" at the vertices and removing an edge if the sum of the powers at its endpoints is at least its weight. The objective is to minimize the sum of the assigned powers. MSPEC is a graph generalization of a barrier coverage problem in a wireless sensor network: given a set of unit disks with centers in a rectangle, what is the minimum total amount by which we must shrink the disks to permit an intruder to cross the rectangle undetected, i.e. without entering any disc. This is a more sophisticated measure of barrier coverage than the minimum number of disks whose removal breaks the barrier. We develop a fully polynomial time approximation scheme (FPTAS) for MSPEC. We give polynomial time algorithms for the special cases where the edge weights are uniform, or the power values are restricted to a bounded set. Although MSPEC is related to network flow and matching problems, its computational complexity (in P or NP-hard) remains open

    Urban food strategies in Central and Eastern Europe: what's specific and what's at stake?

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    Integrating a larger set of instruments into Rural Development Programmes implied an increasing focus on monitoring and evaluation. Against the highly diversified experience with regard to implementation of policy instruments the Common Monitoring and Evaluation Framework has been set up by the EU Commission as a strategic and streamlined method of evaluating programmes’ impacts. Its indicator-based approach mainly reflects the concept of a linear, measure-based intervention logic that falls short of the true nature of RDP operation and impact capacity on rural changes. Besides the different phases of the policy process, i.e. policy design, delivery and evaluation, the regional context with its specific set of challenges and opportunities seems critical to the understanding and improvement of programme performance. In particular the role of local actors can hardly be grasped by quantitative indicators alone, but has to be addressed by assessing processes of social innovation. This shift in the evaluation focus underpins the need to take account of regional implementation specificities and processes of social innovation as decisive elements for programme performance.

    The Supraoptimization of Design Thinking: An intentional shift towards complexity

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    First introduced decades ago, the term “design thinking” has been used to describe the ways designers think, how non-designers can think like designers, and how organizations can embrace design to become more complex-capable. The research project sought to identify and validate the core competencies related to design thinking. An online questionnaire was used to validate a set of six mindset themes identified in the literature review and to reveal how they are connected. A design probe activity was used to understand how individuals can develop in each of the six mindset themes. Despite a limited sample size, the data revealed promising connections between the mindsets themes. User Focus, Diversity and Problem Framing appeared to be the three core mindset themes with a sixth mindset theme, Process Wayfinding, acting as a balancing force. The research project concludes with recommendations on the role of design thinking for organizations, how individuals can understand and improve their capacity for design thinking, and how a design thinking instrument could support both of these goals

    Proceedings of the 94th Annual Virginia Academy of Science Meeting, 2016

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    Full proceedings of the 94th Annual Virginia Academy of Science Meeting, May 18-20, 2016, at University of Mary Washington, Fredericksburg, VA

    Safety and Reliability - Safe Societies in a Changing World

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    The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

    Climate-Smart Food

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    This open access book asks just how climate-smart our food really is. It follows an average day's worth of food and drink to see where it comes from, how far it travels, and the carbon price we all pay for it. From our breakfast tea and toast, through breaktime chocolate bar, to take-away supper, Dave Reay explores the weather extremes the world’s farmers are already dealing with, and what new threats climate change will bring. Readers will encounter heat waves and hurricanes, wildfires and deadly toxins, as well as some truly climate-smart solutions. In every case there are responses that could cut emissions while boosting resilience and livelihoods. Ultimately we are all in this together, our decisions on what food we buy and how we consume it send life-changing ripples right through the global web that is our food supply. As we face a future of 10 billion mouths to feed in a rapidly changing climate, it’s time to get to know our farmers and herders, our vintners and fisherfolk, a whole lot better.
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