Stabbing Convex Polygons with a Segment or a Polygon

Agarwal, Pankaj K.; Chen, Danny Z.; Ganjugunte, Shashidhara K.; Misiołek, Ewa; Sharir, Micha; Tang, Kai

doi:10.1007/978-3-540-87744-8_5

Cited by 8 publications

(10 citation statements)

References 10 publications

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“…For compound components, one can apply the algorithm MAXIMPACTLOCATION using the function f (q, ·) for each compound component q, as defined in (1). Function f takes into account that a single component failure within the compound component is enough to break down the entire component.…”

Section: Extensions To the Compound Component Casementioning

confidence: 99%

“…We then use a randomized divide-andconquer algorithm to check if the maximum weighted depth (with respect to weights ν) in the arrangement A(R) is at most τ . For example, the algorithm of Agarwal et al [1] can be adopted for this purpose. Since the number of distinct superlevel-sets in R is at most |Λ|, the expected running time of this procedure is O( |Λ| ε 2 log 2 |Λ| ε ).…”

Section: Improving Running Time By Samplingmentioning

confidence: 99%

“…The probability that a component is affected by the attacks depends on various factors, such as the distance from the attack's epicenter to the component, the topography of the surrounding area, the component's specifications, and even its location within a building or a system. 1 We consider arbitrary probability functions (with constant description complexity) and develop algorithms that obtain the expected vulnerability of the network. Furthermore, while [17], [24]- [26], [31], [32], [37] consider only a single event, our algorithms allow the assessment of the effects of several simultaneous events.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Resilience of WDM Networks to Probabilistic Geographical Failures

Agarwal

Efrat

Ganjugunte

et al. 2013

IEEE/ACM Trans. Networking

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142

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Abstract-Telecommunications networks, and in particular optical WDM networks, are vulnerable to large-scale failures of their physical infrastructure, resulting from physical attacks (such as an Electromagnetic Pulse attack) or natural disasters (such as solar flares, earthquakes, and floods). Such events happen at specific geographical locations and disrupt specific parts of the network but their effects are not deterministic. Therefore, we provide a unified framework to model the network vulnerability when the event has a probabilistic nature, defined by an arbitrary probability density function. Our framework captures scenarios with a number of simultaneous attacks, in which network components consist of several dependent subcomponents, and in which either a 1+1 or a 1:1 protection plan is in place. We use computational geometric tools to provide efficient algorithms to identify vulnerable points within the network under various metrics. Then, we obtain numerical results for specific backbone networks, thereby demonstrating the applicability of our algorithms to real-world scenarios. Our novel approach allows for identifying locations which require additional protection efforts (e.g., equipment shielding). Overall, the paper demonstrates that using computational geometric techniques can significantly contribute to our understanding of network resilience.

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Section: Extensions To the Compound Component Casementioning

confidence: 99%

Section: Improving Running Time By Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Resilience of WDM Networks to Probabilistic Geographical Failures

Agarwal

Efrat

Ganjugunte

et al. 2013

IEEE/ACM Trans. Networking

Self Cite

142

View full text Add to dashboard Cite

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“…We note that it is unnecessary to compute A(L i ) in each step. Instead we can compute A(L) at the beginning and maintain A(L i ) and the depth of each of its vertices using a dynamic data structure; see [2]. The asymptotic running time now becomes O(m 2 nς log 2 n), which is faster if |S| ≥ log n.…”

Section: The Greedy Algorithmmentioning

confidence: 99%

“…it can be shown that the number of iterations then is still O(h ln |L|) [2]. Using this observation, we can expedite the algorithm if ∆(L i ) is large, as follows: We choose a random subset K i ⊂ L i of smaller size (which is inversely proportional to ∆(L i )) and set z i to be a deepest point with respect to…”

Section: The Greedy Algorithmmentioning

confidence: 99%

Efficient Sensor Placement for Surveillance Problems

Agarwal

Ezra

Ganjugunte

2009

Distributed Computing in Sensor Systems

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Abstract. We study the problem of covering a two-dimensional spatial region P , cluttered with occluders, by sensors. A sensor placed at a location p covers a point x in P if x lies within sensing radius r from p and x is visible from p, i.e., the segment px does not intersect any occluder. The goal is to compute a placement of the minimum number of sensors that cover P . We propose a landmark-based approach for covering P . Suppose P has ς holes, and it can be covered by h sensors. Given a small parameter ε > 0, let λ := λ(h, ε) = (h/ε) log ς. We prove that one can compute a set L of O(λ log λ log (1/ε)) landmarks so that if a set S of sensors covers L, then S covers at least (1 − ε)-fraction of P . It is surprising that so few landmarks are needed, and that the number does not depend on the number of vertices in P . We then present efficient randomized algorithms, based on the greedy approach, that, with high probability, compute O(h log λ) sensor locations to cover L; hereh ≤ h is the number sensors needed to cover L. We propose various extensions of our approach, including: (i) a weight function over P is given and S should cover at least (1 − ε) of the weighted area of P , and (ii) each point of P is covered by at least t sensors, for a given parameter t ≥ 1.

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