The Experts below are selected from a list of 19080 Experts worldwide ranked by ideXlab platform
Frans Schalekamp - One of the best experts on this subject based on the ideXlab platform.
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brief announcement on the complexity of the minimum latency scheduling problem on the Euclidean Plane
ACM Symposium on Parallel Algorithms and Architectures, 2012Co-Authors: Henry Lin, Frans SchalekampAbstract:We announce NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a given threshold. In the MLS problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NP-hard, when the nodes are known to be placed in the Euclidean Plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values alpha >= 3.
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on the complexity of the minimum latency scheduling problem on the Euclidean Plane
arXiv: Networking and Internet Architecture, 2012Co-Authors: Henry Lin, Frans SchalekampAbstract:We show NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a given threshold. In the minimum latency scheduling problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NP-hard, when the nodes are placed in the Euclidean Plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values $\alpha \geq 3$.
Bang-yen Chen - One of the best experts on this subject based on the ideXlab platform.
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lagrangian surfaces in complex Euclidean Plane via spherical and hyperbolic curves
Tohoku Mathematical Journal, 2006Co-Authors: Ildefonso Castro, Bang-yen ChenAbstract:We present a method to construct a large family of Lagrangian surfaces in complex Euclidean Plane $\boldsymbol{C}^2$ by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in $\boldsymbol{C}^2$.
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lagrangian surfaces in complex Euclidean Plane via spherical and hyperbolic curves
arXiv: Differential Geometry, 2006Co-Authors: Ildefonso Castro, Bang-yen ChenAbstract:We present a method to construct a large family of Lagrangian surfaces in complex Euclidean Plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in complex Euclidean Plane.
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construction of lagrangian surfaces in complex Euclidean Plane with legendre curves
Kodai Mathematical Journal, 2006Co-Authors: Bang-yen ChenAbstract:An important problem in the theory of Lagrangian submanifolds is to find non-trivial examples of Lagrangian submanifolds in complex Euclidean spaces with some given special geometric properties. In this article, we provide a new method to construct Lagrangian surfaces in the complex Euclidean Plane C2 by using Legendre curves in S3(1) $\subset$ C2. We also investigate intrinsic and extrinsic geometric properties of the Lagrangian surfaces in C2 obtained by applying our construction method. As an application we provide some new families of Hamiltonian minimal Lagrangian surfaces in C2 via our construction method.
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CLASSIFICATION OF LAGRANGIAN SURFACES OF CONSTANT CURVATURE IN THE COMPLEX Euclidean Plane
Proceedings of the Edinburgh Mathematical Society, 2005Co-Authors: Bang-yen ChenAbstract:One of the most fundamental problems in the study of Lagrangian submanifolds from a Riemannian geometric point of view is the classification of Lagrangian immersions of real-space forms into complex-space forms. In this article, we solve this problem for the most basic case; namely, we classify Lagrangian surfaces of constant curvature in the complex Euclidean Plane $\mathbb{C}^2$. Our main result states that there exist 19 families of Lagrangian surfaces of constant curvature in $\mathbb{C}^2$. Twelve of the 19 families are obtained via Legendre curves. Conversely, Lagrangian surfaces of constant curvature in $\mathbb{C}^2$ can be obtained locally from the 19 families.
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Lagrangian surfaces of constant curvature in complex Euclidean Plane
Tohoku Mathematical Journal, 2004Co-Authors: Bang-yen ChenAbstract:In this article we completely classify Lagrangian H -umbilical surfaces of constant curvature in complex Euclidean Plane.
Darren Strash - One of the best experts on this subject based on the ideXlab platform.
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succinct greedy geometric routing in the Euclidean Plane
International Symposium on Algorithms and Computation, 2009Co-Authors: Michael T Goodrich, Darren StrashAbstract:We show that greedy geometric routing schemes exist for the Euclidean metric in R 2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(logn) bits, where n is the number of vertices in the graph.
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succinct greedy geometric routing in the Euclidean Plane
arXiv: Computational Geometry, 2008Co-Authors: Michael T Goodrich, Darren StrashAbstract:In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. We show that greedy geometric routing schemes exist for the Euclidean metric in R^2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits, where n is the number of vertices in the graph. Moreover, our embedding strategy introduces a coordinate system for R^2 that supports distance comparisons using our succinct coordinates. Thus, our scheme can be used to significantly reduce bandwidth, space, and header size over other recently discovered greedy geometric routing implementations for R^2.
Kyung-yong Chwa - One of the best experts on this subject based on the ideXlab platform.
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VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE Euclidean Plane
International Journal of Computational Geometry & Applications, 2006Co-Authors: Sang Won Bae, Kyung-yong ChwaAbstract:This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean Plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2 + m3 + nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean Plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2 + n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space.
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voronoi diagrams with a transportation network on the Euclidean Plane
International Symposium on Algorithms and Computation, 2004Co-Authors: Sang Won Bae, Kyung-yong ChwaAbstract:This paper investigates geometric and algorithmic properties of the Voronoi diagram with a transportation network on the Euclidean Plane With a transportation network, the distance is measured as the length of the shortest (time) path In doing so, we introduce a needle, a generalized Voronoi site We present an O(nm2log n + m3log m) algorithm to compute the Voronoi diagram with a transportation network on the Euclidean Plane, where n is the number of given sites and m is the complexity of the given transportation network.
Henry Lin - One of the best experts on this subject based on the ideXlab platform.
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brief announcement on the complexity of the minimum latency scheduling problem on the Euclidean Plane
ACM Symposium on Parallel Algorithms and Architectures, 2012Co-Authors: Henry Lin, Frans SchalekampAbstract:We announce NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a given threshold. In the MLS problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NP-hard, when the nodes are known to be placed in the Euclidean Plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values alpha >= 3.
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on the complexity of the minimum latency scheduling problem on the Euclidean Plane
arXiv: Networking and Internet Architecture, 2012Co-Authors: Henry Lin, Frans SchalekampAbstract:We show NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a given threshold. In the minimum latency scheduling problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NP-hard, when the nodes are placed in the Euclidean Plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values $\alpha \geq 3$.