### Abstract

We consider rigid and globally rigid bar-and-joint frameworks (resp. graphs) in which some joints (resp. vertices) are pinned down and hence their positions are fixed. We give an overview of some old and new results of this branch of combinatorial rigidity with an emphasis on the related optimization problems. In one of these problems the goal is to find a set P of vertices of minimum total cost for which the positions of all vertices become uniquely determined when P is pinned down. For this problem, which is motivated by the localization problem in wireless sensor networks, we give a constant factor approximation algorithm.

Original language | English |
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Title of host publication | Bolyai Society Mathematical Studies |

Pages | 151-172 |

Number of pages | 22 |

Volume | 20 |

DOIs | |

Publication status | Published - 2010 |

Event | Meeting on Fete of Combinatorics and Computer Science - Keszthely, Hungary Duration: Aug 11 2008 → Aug 15 2008 |

### Other

Other | Meeting on Fete of Combinatorics and Computer Science |
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Country | Hungary |

City | Keszthely |

Period | 8/11/08 → 8/15/08 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Bolyai Society Mathematical Studies*(Vol. 20, pp. 151-172) https://doi.org/10.1007/978-3-642-13580-4_7

**Rigid and globally rigid graphs with pinned vertices.** / Jordán, T.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Bolyai Society Mathematical Studies.*vol. 20, pp. 151-172, Meeting on Fete of Combinatorics and Computer Science, Keszthely, Hungary, 8/11/08. https://doi.org/10.1007/978-3-642-13580-4_7

}

TY - GEN

T1 - Rigid and globally rigid graphs with pinned vertices

AU - Jordán, T.

PY - 2010

Y1 - 2010

N2 - We consider rigid and globally rigid bar-and-joint frameworks (resp. graphs) in which some joints (resp. vertices) are pinned down and hence their positions are fixed. We give an overview of some old and new results of this branch of combinatorial rigidity with an emphasis on the related optimization problems. In one of these problems the goal is to find a set P of vertices of minimum total cost for which the positions of all vertices become uniquely determined when P is pinned down. For this problem, which is motivated by the localization problem in wireless sensor networks, we give a constant factor approximation algorithm.

AB - We consider rigid and globally rigid bar-and-joint frameworks (resp. graphs) in which some joints (resp. vertices) are pinned down and hence their positions are fixed. We give an overview of some old and new results of this branch of combinatorial rigidity with an emphasis on the related optimization problems. In one of these problems the goal is to find a set P of vertices of minimum total cost for which the positions of all vertices become uniquely determined when P is pinned down. For this problem, which is motivated by the localization problem in wireless sensor networks, we give a constant factor approximation algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84880271989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880271989&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13580-4_7

DO - 10.1007/978-3-642-13580-4_7

M3 - Conference contribution

AN - SCOPUS:84880271989

SN - 9783642135798

VL - 20

SP - 151

EP - 172

BT - Bolyai Society Mathematical Studies

ER -