2 Search Results for "Lin, Patrick"


Document
A Toroidal Maxwell-Cremona-Delaunay Correspondence

Authors: Jeff Erickson and Patrick Lin

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
We consider three classes of geodesic embeddings of graphs on Euclidean flat tori: - A torus graph G is equilibrium if it is possible to place positive weights on the edges, such that the weighted edge vectors incident to each vertex of G sum to zero. - A torus graph G is reciprocal if there is a geodesic embedding of the dual graph G^* on the same flat torus, where each edge of G is orthogonal to the corresponding dual edge in G^*. - A torus graph G is coherent if it is possible to assign weights to the vertices, so that G is the (intrinsic) weighted Delaunay graph of its vertices. The classical Maxwell-Cremona correspondence and the well-known correspondence between convex hulls and weighted Delaunay triangulations imply that the analogous concepts for plane graphs (with convex outer faces) are equivalent. Indeed, all three conditions are equivalent to G being the projection of the 1-skeleton of the lower convex hull of points in ℝ³. However, this three-way equivalence does not extend directly to geodesic graphs on flat tori. On any flat torus, reciprocal and coherent graphs are equivalent, and every reciprocal graph is equilibrium, but not every equilibrium graph is reciprocal. We establish a weaker correspondence: Every equilibrium graph on any flat torus is affinely equivalent to a reciprocal/coherent graph on some flat torus.

Cite as

Jeff Erickson and Patrick Lin. A Toroidal Maxwell-Cremona-Delaunay Correspondence. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{erickson_et_al:LIPIcs.SoCG.2020.40,
  author =	{Erickson, Jeff and Lin, Patrick},
  title =	{{A Toroidal Maxwell-Cremona-Delaunay Correspondence}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.40},
  URN =		{urn:nbn:de:0030-drops-121984},
  doi =		{10.4230/LIPIcs.SoCG.2020.40},
  annote =	{Keywords: combinatorial topology, geometric graphs, homology, flat torus, spring embedding, intrinsic Delaunay}
}
Document
An Architecture for Tetherless Communication

Authors: Aaditeshwar Seth, Patrick Darragh, Suihong Liang, Yunfeng Lin, and Srinivasan Keshav

Published in: Dagstuhl Seminar Proceedings, Volume 5142, Disruption Tolerant Networking (2005)


Abstract
In the emerging paradigm of tetherless computing, client applications running on small, inexpensive, and smart mobile devices maintain opportunistic wireless connectivity with back-end services running on centralized computers, enabling novel classes of applications. These applications require a communications infrastrastructure that is mobility-aware, disconnection-resilient and provides support for an opportunistic style of communiction. It should even be able to function across network partitions that may arise when end-to-end communication is not possible. We outline, design, and evaluate the implementation of an architecture that provides this functionality. we shot that it is possible for next-generation mobile devices to obtain up to 80-fold improvement over conventional mechanisms by exploiting opportunistic WiFi links, and that this benefit can be delivered as an overlay that is compatible with the current Internet.

Cite as

Aaditeshwar Seth, Patrick Darragh, Suihong Liang, Yunfeng Lin, and Srinivasan Keshav. An Architecture for Tetherless Communication. In Disruption Tolerant Networking. Dagstuhl Seminar Proceedings, Volume 5142, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{seth_et_al:DagSemProc.05142.3,
  author =	{Seth, Aaditeshwar and Darragh, Patrick and Liang, Suihong and Lin, Yunfeng and Keshav, Srinivasan},
  title =	{{An Architecture for Tetherless Communication}},
  booktitle =	{Disruption Tolerant Networking},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5142},
  editor =	{Marcus Brunner and Lars Eggert and Kevin Fall and J\"{o}rg Ott and Lars Wolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05142.3},
  URN =		{urn:nbn:de:0030-drops-3519},
  doi =		{10.4230/DagSemProc.05142.3},
  annote =	{Keywords: Delay tolerant networks, Opportunistic communication, Tetherless computing, Wireless, Mobile}
}
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