Dagstuhl Seminar Proceedings, Volume 6481
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
6481
2007
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-6481
06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings
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.
Geometric networks
metric space embeddings
phylogenetic networks
spanners
dilation
distortion
1-21
Regular Paper
Joachim
Gudmundsson
Joachim Gudmundsson
Rolf
Klein
Rolf Klein
Giri
Narasimhan
Giri Narasimhan
Michiel
Smid
Michiel Smid
Alexander
Wolff
Alexander Wolff
10.4230/DagSemProc.06481.1
Creative Commons Attribution 4.0 International license
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Geometric Distance Estimation for Sensor Networks and Unit Disk Graphs
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.
Sensor networks
distance estimation
unit disk graphs.
1-2
Regular Paper
Sándor
Fekete
Sándor Fekete
Alexander
Kröller
Alexander Kröller
Carsten
Buschmann
Carsten Buschmann
Stefan
Fischer
Stefan Fischer
10.4230/DagSemProc.06481.2
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Power Assignment in Radio Networks with Two Power Levels
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.
Radio networks
power assignment
approximation algorithms
minimum spanning tree
disk graph
1-18
Regular Paper
Paz
Carmi
Paz Carmi
Matthew
Katz
Matthew Katz
10.4230/DagSemProc.06481.3
Creative Commons Attribution 4.0 International license
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