DC Field | Value | Language |
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dc.contributor.author | Schindelhauer, Christian | ko |

dc.contributor.author | Volbert, Klaus | ko |

dc.contributor.author | Ziegler, Martin | ko |

dc.date.accessioned | 2016-04-12T07:52:09Z | - |

dc.date.available | 2016-04-12T07:52:09Z | - |

dc.date.created | 2015-09-17 | - |

dc.date.created | 2015-09-17 | - |

dc.date.issued | 2007-04 | - |

dc.identifier.citation | COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.36, no.3, pp.197 - 214 | - |

dc.identifier.issn | 0925-7721 | - |

dc.identifier.uri | http://hdl.handle.net/10203/203398 | - |

dc.description.abstract | In this paper we investigate the relations between spanners, weak spanners, and power spanners in R-D for any dimension D and apply our results to topology control in wireless networks. For c is an element of R, a c-spanner is a subgraph of the complete Euclidean graph satisfying the condition that between any two vertices there exists a path of length at most c-times their Euclidean distance. Based on this ability to approximate the complete Euclidean graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks. In a weak c-spanner, this path may be arbitrarily long, but must remain within a disk or sphere of radius c-times the Euclidean distance between the vertices. Finally in a c-power spanner, the total energy consumed on Such a path, where the energy is given by the sum of the squares of the edge lengths on this path, must be at most c-times the square of the Euclidean distance of the direct edge or communication link. While it is known that any c-spanner is also both a weak C-1-spanner and a C-2-power spanner for appropriate C-1, C-2 depending only on c but not on the graph under consideration, we show that the converse is not true: there exists a family of c(1)-power spanners that are not weak C-spanners and also a family of weak c(2)-spanners that are not C-spanners for any fixed C. However a main result of this paper reveals that any weak c-spanner is also a C-power spanner for an appropriate constant C. We further generalize the latter notion by considering (c, delta)-power spanners where the sum of the delta th powers of the lengths has to be bounded, so (c, 2)-power spanners coincide with the usual power spanners and (c, I)-power spanners are classical spanners. Interestingly, these (c, delta)-power spanners form a strict hierarchy where the above results still hold for any delta >= D some even hold for delta > 1 while counter-examples exist for delta < D. We show that every self-similar curve of fractal dimension D-f >= delta is not a (C, delta)-power spanner for any fixed C, in general. Finally, we consider the sparsified Yao-graph (SparsY-graph or YY) that is a well-known sparse topology for wireless networks. We prove that all SparsY-graphs are weak c-spanners for a constant c and hence they allow us to approximate energy-optimal wireless networks by a constant factor. (c) 2006 Elsevier B.V. All rights reserved. | - |

dc.language | English | - |

dc.publisher | ELSEVIER SCIENCE BV | - |

dc.subject | AD HOC NETWORKS | - |

dc.title | Geometric spanners with applications in wireless networks | - |

dc.type | Article | - |

dc.identifier.wosid | 000244221700004 | - |

dc.identifier.scopusid | 2-s2.0-84867970573 | - |

dc.type.rims | ART | - |

dc.citation.volume | 36 | - |

dc.citation.issue | 3 | - |

dc.citation.beginningpage | 197 | - |

dc.citation.endingpage | 214 | - |

dc.citation.publicationname | COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | - |

dc.identifier.doi | 10.1016/j.comgeo.2006.02.001 | - |

dc.contributor.localauthor | Ziegler, Martin | - |

dc.contributor.nonIdAuthor | Schindelhauer, Christian | - |

dc.contributor.nonIdAuthor | Volbert, Klaus | - |

dc.type.journalArticle | Article; Proceedings Paper | - |

dc.subject.keywordPlus | AD HOC NETWORKS | - |

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