Volume

Dagstuhl Seminar Proceedings, Volume 6481



Publication Details

  • published at: 2007-06-01
  • Publisher: Schloss-Dagstuhl - Leibniz Zentrum für Informatik

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06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings

Authors: Joachim Gudmundsson, Rolf Klein, Giri Narasimhan, Michiel Smid, and Alexander Wolff


Abstract
The Dagstuhl Seminar 06481 ``Geometric Networks and Metric Space Embeddings'' was held from November~26 to December~1, 2006 in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. In this paper we describe the seminar topics, we have compiled a list of open questions that were posed during the seminar, there is a list of all talks and there are abstracts of the presentations given during the seminar. Links to extended abstracts or full papers are provided where available.

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Joachim Gudmundsson, Rolf Klein, Giri Narasimhan, Michiel Smid, and Alexander Wolff. 06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings. In Geometric Networks and Metric Space Embeddings. Dagstuhl Seminar Proceedings, Volume 6481, pp. 1-21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{gudmundsson_et_al:DagSemProc.06481.1,
  author =	{Gudmundsson, Joachim and Klein, Rolf and Narasimhan, Giri and Smid, Michiel and Wolff, Alexander},
  title =	{{06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings}},
  booktitle =	{Geometric Networks and Metric Space Embeddings},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6481},
  editor =	{Joachim Gudmundsson and Rolf Klein and Giri Narasimhan and Michiel Smid and Alexander Wolff},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06481.1},
  URN =		{urn:nbn:de:0030-drops-10291},
  doi =		{10.4230/DagSemProc.06481.1},
  annote =	{Keywords: Geometric networks, metric space embeddings, phylogenetic networks, spanners, dilation, distortion}
}
Document
Geometric Distance Estimation for Sensor Networks and Unit Disk Graphs

Authors: Sándor Fekete, Alexander Kröller, Carsten Buschmann, and Stefan Fischer


Abstract
We present an approach to estimating distances in sensor networks. It works by counting common neighbors, high values indicating closeness. Such distance estimates are needed in many self-localization algorithms. Other than many other approaches, ours does not rely on special equipment in the devices.

Cite as

Sándor Fekete, Alexander Kröller, Carsten Buschmann, and Stefan Fischer. Geometric Distance Estimation for Sensor Networks and Unit Disk Graphs. In Geometric Networks and Metric Space Embeddings. Dagstuhl Seminar Proceedings, Volume 6481, pp. 1-2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{fekete_et_al:DagSemProc.06481.2,
  author =	{Fekete, S\'{a}ndor and Kr\"{o}ller, Alexander and Buschmann, Carsten and Fischer, Stefan},
  title =	{{Geometric Distance Estimation for Sensor Networks and Unit Disk Graphs}},
  booktitle =	{Geometric Networks and Metric Space Embeddings},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6481},
  editor =	{Joachim Gudmundsson and Rolf Klein and Giri Narasimhan and Michiel Smid and Alexander Wolff},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06481.2},
  URN =		{urn:nbn:de:0030-drops-10282},
  doi =		{10.4230/DagSemProc.06481.2},
  annote =	{Keywords: Sensor networks, distance estimation, unit disk graphs.}
}
Document
Power Assignment in Radio Networks with Two Power Levels

Authors: Paz Carmi and Matthew Katz


Abstract
We study the power assignment problem in radio networks, where each radio station can transmit in one of two possible power levels, corresponding to two ranges - short and long. We show that this problem is NP-hard, and present an O(n^2)-time assignment algorithm, such that the number of transmitters that are assigned long range by the algorithm is at most (11/6) times the number of transmitters that are assigned long range by an optimal algorithm. We also present an (9/5)-approximation algorithm for this problem whose running time is considerably higher. Next, we formulate and study the Minimum-Area Spanning Tree (MAST)problem: Given a set P of n points in the plane, find a spanning tree of P of minimum "area," where the area of a spanning tree T is the area of the union of the n-1 disks whose diameters are the edges in T. We prove that the Euclidean minimum spanning tree of P is a constant-factor approximation for MAST. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (MARA) problem, for the Minimum-Area Connected Disk Graph (MACDG) problem, and for the Minimum-Area Tour (MAT) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.

Cite as

Paz Carmi and Matthew Katz. Power Assignment in Radio Networks with Two Power Levels. In Geometric Networks and Metric Space Embeddings. Dagstuhl Seminar Proceedings, Volume 6481, pp. 1-18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)


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@InProceedings{carmi_et_al:DagSemProc.06481.3,
  author =	{Carmi, Paz and Katz, Matthew},
  title =	{{Power Assignment in Radio Networks with Two Power Levels}},
  booktitle =	{Geometric Networks and Metric Space Embeddings},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6481},
  editor =	{Joachim Gudmundsson and Rolf Klein and Giri Narasimhan and Michiel Smid and Alexander Wolff},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06481.3},
  URN =		{urn:nbn:de:0030-drops-10277},
  doi =		{10.4230/DagSemProc.06481.3},
  annote =	{Keywords: Radio networks, power assignment, approximation algorithms, minimum spanning tree, disk graph}
}

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