27 Search Results for "Klein, Rolf"


Document
An Experimental Study of External Memory Algorithms for Connected Components

Authors: Gerth Stølting Brodal, Rolf Fagerberg, David Hammer, Ulrich Meyer, Manuel Penschuck, and Hung Tran

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)


Abstract
We empirically investigate algorithms for solving Connected Components in the external memory model. In particular, we study whether the randomized O(Sort(E)) algorithm by Karger, Klein, and Tarjan can be implemented to compete with practically promising and simpler algorithms having only slightly worse theoretical cost, namely Borůvka’s algorithm and the algorithm by Sibeyn and collaborators. For all algorithms, we develop and test a number of tuning options. Our experiments are executed on a large set of different graph classes including random graphs, grids, geometric graphs, and hyperbolic graphs. Among our findings are: The Sibeyn algorithm is a very strong contender due to its simplicity and due to an added degree of freedom in its internal workings when used in the Connected Components setting. With the right tunings, the Karger-Klein-Tarjan algorithm can be implemented to be competitive in many cases. Higher graph density seems to benefit Karger-Klein-Tarjan relative to Sibeyn. Borůvka’s algorithm is not competitive with the two others.

Cite as

Gerth Stølting Brodal, Rolf Fagerberg, David Hammer, Ulrich Meyer, Manuel Penschuck, and Hung Tran. An Experimental Study of External Memory Algorithms for Connected Components. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{brodal_et_al:LIPIcs.SEA.2021.23,
  author =	{Brodal, Gerth St{\o}lting and Fagerberg, Rolf and Hammer, David and Meyer, Ulrich and Penschuck, Manuel and Tran, Hung},
  title =	{{An Experimental Study of External Memory Algorithms for Connected Components}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{23:1--23:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.23},
  URN =		{urn:nbn:de:0030-drops-137958},
  doi =		{10.4230/LIPIcs.SEA.2021.23},
  annote =	{Keywords: Connected Components, Experimental Evaluation, External Memory, Graph Algorithms, Randomization}
}
Document
On the Stretch Factor of Polygonal Chains

Authors: Ke Chen, Adrian Dumitrescu, Wolfgang Mulzer, and Csaba D. Tóth

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
Let P=(p_1, p_2, ..., p_n) be a polygonal chain. The stretch factor of P is the ratio between the total length of P and the distance of its endpoints, sum_{i = 1}^{n-1} |p_i p_{i+1}|/|p_1 p_n|. For a parameter c >= 1, we call P a c-chain if |p_ip_j|+|p_jp_k| <= c|p_ip_k|, for every triple (i,j,k), 1 <= i<j<k <= n. The stretch factor is a global property: it measures how close P is to a straight line, and it involves all the vertices of P; being a c-chain, on the other hand, is a fingerprint-property: it only depends on subsets of O(1) vertices of the chain. We investigate how the c-chain property influences the stretch factor in the plane: (i) we show that for every epsilon > 0, there is a noncrossing c-chain that has stretch factor Omega(n^{1/2-epsilon}), for sufficiently large constant c=c(epsilon); (ii) on the other hand, the stretch factor of a c-chain P is O(n^{1/2}), for every constant c >= 1, regardless of whether P is crossing or noncrossing; and (iii) we give a randomized algorithm that can determine, for a polygonal chain P in R^2 with n vertices, the minimum c >= 1 for which P is a c-chain in O(n^{2.5} polylog n) expected time and O(n log n) space.

Cite as

Ke Chen, Adrian Dumitrescu, Wolfgang Mulzer, and Csaba D. Tóth. On the Stretch Factor of Polygonal Chains. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chen_et_al:LIPIcs.MFCS.2019.56,
  author =	{Chen, Ke and Dumitrescu, Adrian and Mulzer, Wolfgang and T\'{o}th, Csaba D.},
  title =	{{On the Stretch Factor of Polygonal Chains}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{56:1--56:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.56},
  URN =		{urn:nbn:de:0030-drops-110005},
  doi =		{10.4230/LIPIcs.MFCS.2019.56},
  annote =	{Keywords: polygonal chain, vertex dilation, Koch curve, recursive construction}
}
Document
Partially Walking a Polygon

Authors: Franz Aurenhammer, Michael Steinkogler, and Rolf Klein

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)


Abstract
Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Theta(n) such maximal walks, and we show how to find all of them in O(n log n) time.

Cite as

Franz Aurenhammer, Michael Steinkogler, and Rolf Klein. Partially Walking a Polygon. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 60:1-60:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{aurenhammer_et_al:LIPIcs.ISAAC.2018.60,
  author =	{Aurenhammer, Franz and Steinkogler, Michael and Klein, Rolf},
  title =	{{Partially Walking a Polygon}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{60:1--60:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.60},
  URN =		{urn:nbn:de:0030-drops-100089},
  doi =		{10.4230/LIPIcs.ISAAC.2018.60},
  annote =	{Keywords: Polygon, guard walk, visibility}
}
Document
An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams

Authors: Cecilia Bohler, Rolf Klein, and Chih-Hung Liu

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)


Abstract
Given a set of n sites in the plane, the order-k Voronoi diagram is a planar subdivision such that all points in a region share the same k nearest sites. The order-k Voronoi diagram arises for the k-nearest-neighbor problem, and there has been a lot of work for point sites in the Euclidean metric. In this paper, we study order-k Voronoi diagrams defined by an abstract bisecting curve system that satisfies several practical axioms, and thus our study covers many concrete order-k Voronoi diagrams. We propose a randomized incremental construction algorithm that runs in O(k(n-k) log^2 n +n log^3 n) steps, where O(k(n-k)) is the number of faces in the worst case. Due to those axioms, this result applies to disjoint line segments in the L_p norm, convex polygons of constant size, points in the Karlsruhe metric, and so on. In fact, this kind of run time with a polylog factor to the number of faces was only achieved for point sites in the L_1 or Euclidean metric before.

Cite as

Cecilia Bohler, Rolf Klein, and Chih-Hung Liu. An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bohler_et_al:LIPIcs.SoCG.2016.21,
  author =	{Bohler, Cecilia and Klein, Rolf and Liu, Chih-Hung},
  title =	{{An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.21},
  URN =		{urn:nbn:de:0030-drops-59135},
  doi =		{10.4230/LIPIcs.SoCG.2016.21},
  annote =	{Keywords: Order-k Voronoi Diagrams, Abstract Voronoi Diagrams, Randomized Geometric Algorithms}
}
Document
A Fire Fighter’s Problem

Authors: Rolf Klein, Elmar Langetepe, and Christos Levcopoulos

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)


Abstract
Suppose that a circular fire spreads in the plane at unit speed. A fire fighter can build a barrier at speed v > 1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We provide two results. First, we analyze the natural strategy where the fighter keeps building a barrier along the frontier of the expanding fire. We prove that this approach contains the fire if v > v_c = 2.6144... holds. Second, we show that any "spiralling" strategy must have speed v > 1.618, the golden ratio, in order to succeed.

Cite as

Rolf Klein, Elmar Langetepe, and Christos Levcopoulos. A Fire Fighter’s Problem. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 768-780, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{klein_et_al:LIPIcs.SOCG.2015.768,
  author =	{Klein, Rolf and Langetepe, Elmar and Levcopoulos, Christos},
  title =	{{A Fire Fighter’s Problem}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{768--780},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.768},
  URN =		{urn:nbn:de:0030-drops-51044},
  doi =		{10.4230/LIPIcs.SOCG.2015.768},
  annote =	{Keywords: Motion Planning, Dynamic Environments, Spiralling strategies, Lower and upper bounds}
}
Document
09451 Abstracts Collection – Geometric Networks, Metric Space Embeddings and Spatial Data Mining

Authors: Gautam Das, Joachim Gudmundsson, Rolf Klein, Christian Knauer, and Michiel Smid

Published in: Dagstuhl Seminar Proceedings, Volume 9451, Geometric Networks, Metric Space Embeddings and Spatial Data Mining (2010)


Abstract
From November 1 to 6, 2009, the Dagstuhl Seminar 09451 ``Geometric Networks, Metric Space Embeddings and Spatial Data Mining'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Gautam Das, Joachim Gudmundsson, Rolf Klein, Christian Knauer, and Michiel Smid. 09451 Abstracts Collection – Geometric Networks, Metric Space Embeddings and Spatial Data Mining. In Geometric Networks, Metric Space Embeddings and Spatial Data Mining. Dagstuhl Seminar Proceedings, Volume 9451, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{das_et_al:DagSemProc.09451.1,
  author =	{Das, Gautam and Gudmundsson, Joachim and Klein, Rolf and Knauer, Christian and Smid, Michiel},
  title =	{{09451 Abstracts Collection – Geometric Networks, Metric Space Embeddings and Spatial Data Mining}},
  booktitle =	{Geometric Networks, Metric Space Embeddings and Spatial Data Mining},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9451},
  editor =	{Gautam Das and Joachim Gudmundsson and Rolf Klein and Christian Knauer and Michiel Smid},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09451.1},
  URN =		{urn:nbn:de:0030-drops-24380},
  doi =		{10.4230/DagSemProc.09451.1},
  annote =	{Keywords: Geometric networks, metric space embeddings, spatial data mining, spanners, dilation, distortion}
}
Document
09171 Abstracts Collection – Adaptive, Output Sensitive, Online and Parameterized Algorithms

Authors: Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier

Published in: Dagstuhl Seminar Proceedings, Volume 9171, Adaptive, Output Sensitive, Online and Parameterized Algorithms (2009)


Abstract
From 19.01. to 24.04.2009, the Dagstuhl Seminar 09171 ``Adaptive, Output Sensitive, Online and Parameterized Algorithms '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier. 09171 Abstracts Collection – Adaptive, Output Sensitive, Online and Parameterized Algorithms. In Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings, Volume 9171, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{barbay_et_al:DagSemProc.09171.1,
  author =	{Barbay, J\'{e}r\'{e}my and Klein, Rolf and L\'{o}pez-Ortiz, Alejandro and Niedermeier, Rolf},
  title =	{{09171 Abstracts Collection  – Adaptive, Output Sensitive, Online and Parameterized Algorithms}},
  booktitle =	{Adaptive, Output Sensitive, Online and Parameterized Algorithms},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9171},
  editor =	{J\'{e}r\'{e}my Barbay and Rolf Klein and Alejandro Ortiz-L\'{o}pez and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09171.1},
  URN =		{urn:nbn:de:0030-drops-21228},
  doi =		{10.4230/DagSemProc.09171.1},
  annote =	{Keywords: Adaptive analysis, instance optimal algoritms, fixed parameter tractable, output sensitive algorithms}
}
Document
09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms

Authors: Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier

Published in: Dagstuhl Seminar Proceedings, Volume 9171, Adaptive, Output Sensitive, Online and Parameterized Algorithms (2009)


Abstract
Traditionally the analysis of algorithms measures the complexity of a problem or algorithm in terms of the worst-case behavior over all inputs of a given size. However, in certain cases an improved algorithm can be obtained by considering a finer partition of the input space. As this idea has been independently rediscovered in many areas, the workshop gathered participants from different fields in order to explore the impact and the limits of this technique, in the hope to spring new collaboration and to seed the unification of the technique.

Cite as

Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier. 09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms. In Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings, Volume 9171, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{barbay_et_al:DagSemProc.09171.2,
  author =	{Barbay, J\'{e}r\'{e}my and Klein, Rolf and L\'{o}pez-Ortiz, Alejandro and Niedermeier, Rolf},
  title =	{{09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms}},
  booktitle =	{Adaptive, Output Sensitive, Online and Parameterized Algorithms},
  pages =	{1--1},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9171},
  editor =	{J\'{e}r\'{e}my Barbay and Rolf Klein and Alejandro Ortiz-L\'{o}pez and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09171.2},
  URN =		{urn:nbn:de:0030-drops-21207},
  doi =		{10.4230/DagSemProc.09171.2},
  annote =	{Keywords: Adaptive analysis, instance optimal algorithms, fixed parameter tractable, output sensitive algorithms}
}
Document
Parameterized Analysis of Online Steiner Tree Problems

Authors: Spyros Angelopoulos

Published in: Dagstuhl Seminar Proceedings, Volume 9171, Adaptive, Output Sensitive, Online and Parameterized Algorithms (2009)


Abstract
Steiner tree problems occupy a central place in both areas of approximation and on-line algorithms. Many variants have been studied from the point of view of competitive analysis, and for several of these variants tight bounds are known. However, in several cases, worst-case analysis is overly pessimistic, which fails to explain the relative performance of algorithms. We show how adaptive analysis can help resolve this problem. As case studies, we consider the Steiner tree problem in directed graphs, and the Priority Steiner tree problem.

Cite as

Spyros Angelopoulos. Parameterized Analysis of Online Steiner Tree Problems. In Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings, Volume 9171, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{angelopoulos:DagSemProc.09171.3,
  author =	{Angelopoulos, Spyros},
  title =	{{Parameterized Analysis of Online Steiner Tree Problems}},
  booktitle =	{Adaptive, Output Sensitive, Online and Parameterized Algorithms},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9171},
  editor =	{J\'{e}r\'{e}my Barbay and Rolf Klein and Alejandro Ortiz-L\'{o}pez and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09171.3},
  URN =		{urn:nbn:de:0030-drops-21210},
  doi =		{10.4230/DagSemProc.09171.3},
  annote =	{Keywords: Online algorithms, Steiner tree problems, adaptive and parameteried analysis}
}
Document
06481 Abstracts Collection – Geometric Networks and Metric Space Embeddings

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

Published in: Dagstuhl Seminar Proceedings, Volume 6481, Geometric Networks and Metric Space Embeddings (2007)


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.

Cite as

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-dev.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

Published in: Dagstuhl Seminar Proceedings, Volume 6481, Geometric Networks and Metric Space Embeddings (2007)


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-dev.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

Published in: Dagstuhl Seminar Proceedings, Volume 6481, Geometric Networks and Metric Space Embeddings (2007)


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-dev.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}
}
Document
06421 Abstracts Collection – Robot Navigation

Authors: Sándor Fekete, Rudolf Fleischer, Rolf Klein, and Alejandro Lopez-Ortiz

Published in: Dagstuhl Seminar Proceedings, Volume 6421, Robot Navigation (2007)


Abstract
From 15.10.06 to 20.10.06, the Dagstuhl Seminar 06421 ``Robot Navigation''generate automatically was held 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. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Sándor Fekete, Rudolf Fleischer, Rolf Klein, and Alejandro Lopez-Ortiz. 06421 Abstracts Collection – Robot Navigation. In Robot Navigation. Dagstuhl Seminar Proceedings, Volume 6421, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{fekete_et_al:DagSemProc.06421.1,
  author =	{Fekete, S\'{a}ndor and Fleischer, Rudolf and Klein, Rolf and Lopez-Ortiz, Alejandro},
  title =	{{06421 Abstracts Collection – Robot Navigation}},
  booktitle =	{Robot Navigation},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6421},
  editor =	{S\'{a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06421.1},
  URN =		{urn:nbn:de:0030-drops-8890},
  doi =		{10.4230/DagSemProc.06421.1},
  annote =	{Keywords: Motion planning, robotics, computational geometry, online algorithms}
}
Document
06421 Executive Summary – Robot Navigation

Authors: Sándor Fekete, Rudolf Fleischer, Rolf Klein, and Alejandro Lopez-Ortiz

Published in: Dagstuhl Seminar Proceedings, Volume 6421, Robot Navigation (2007)


Abstract
For quite a number of years, researchers from various fields have studied problems motivated by Robot Navigation. People in Online Algorithms have developed strategies that can deal with the inherent lack of information an autonomous robot encounters, as it sets out to perform a task in an unknown environment. Computational Geometers have obtained many results on the efficient planning of collision-free motions, and on visibility problems. Scientists and engineers in Robotics have perfected real robots to an astounding degree. Economic household robots and artificial pets are now available; more complex robots are able to carry out difficult search-and-rescue and exploration missions. The goal of this seminar is to bring together researchers from robotics, computational geometry, and online algorithms, in order to exchange problems and ideas, and to jointly work towards solutions. The following questions seem crucial. Given the advanced level of technical development, what are the strategic planning problems researchers in robotics need to solve in the next decade? How can real environments and robots be modeled, so that planning problems become tractable by algorithmic methods, and solutions are still significant for applications? In particular, what can be assumed about perception and motion accuracy? We are planning for plenary sessions where members of all groups can present their problems and recent work. In addition, there will be plenty of time for discussions.

Cite as

Sándor Fekete, Rudolf Fleischer, Rolf Klein, and Alejandro Lopez-Ortiz. 06421 Executive Summary – Robot Navigation. In Robot Navigation. Dagstuhl Seminar Proceedings, Volume 6421, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{fekete_et_al:DagSemProc.06421.2,
  author =	{Fekete, S\'{a}ndor and Fleischer, Rudolf and Klein, Rolf and Lopez-Ortiz, Alejandro},
  title =	{{06421 Executive Summary – Robot Navigation}},
  booktitle =	{Robot Navigation},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6421},
  editor =	{S\'{a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06421.2},
  URN =		{urn:nbn:de:0030-drops-8720},
  doi =		{10.4230/DagSemProc.06421.2},
  annote =	{Keywords: Motion planning, robotics, computational geometry, online algorithms}
}
Document
6D SLAM with Cached kd-tree Search

Authors: Andreas Nüchter, Kai Lingemann, and Joachim Hertzberg

Published in: Dagstuhl Seminar Proceedings, Volume 6421, Robot Navigation (2007)


Abstract
6D SLAM (Simultaneous Localization and Mapping) or 6D Concurrent Localization and Mapping of mobile robots considers six degrees of freedom for the robot pose, namely, the x, y and z coordinates and the roll, yaw and pitch angles. In previous work we presented our scan matching based 6D SLAM approach, where scan matching is based on the well known iterative closest point (ICP) algorithm [Besl 1992]. Efficient implementations of this algorithm are a result of a fast computation of closest points. The usual approach, i.e., using kd-trees is extended in this paper. We describe a novel search stategy, that leads to significant speed-ups. Our mapping system is real-time capable, i.e., 3D maps are computed using the resources of the used Kurt3D robotic hardware.

Cite as

Andreas Nüchter, Kai Lingemann, and Joachim Hertzberg. 6D SLAM with Cached kd-tree Search. In Robot Navigation. Dagstuhl Seminar Proceedings, Volume 6421, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{nuchter_et_al:DagSemProc.06421.3,
  author =	{N\"{u}chter, Andreas and Lingemann, Kai and Hertzberg, Joachim},
  title =	{{6D SLAM with Cached kd-tree Search}},
  booktitle =	{Robot Navigation},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6421},
  editor =	{S\'{a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06421.3},
  URN =		{urn:nbn:de:0030-drops-8705},
  doi =		{10.4230/DagSemProc.06421.3},
  annote =	{Keywords: SLAM, kd tree search}
}
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