### Abstract

A feed-link is an artificial connection from a given location p to a real-world network. It is most commonly added to an incomplete network to improve the results of network analysis, by making p part of the network. The feed-link has to be "reasonable", hence we use the concept of dilation to determine the quality of a connection. We consider the following abstract problem: Given a simple polygon P with n vertices and a point p inside, determine a point q on P such that adding a feedlink minimizes the maximum dilation of any point on P. Here the dilation of a point r on P is the ratio of the shortest route from r over P and to p, to the Euclidean distance from r to p. We solve this problem in O(λ _{7}(n)logn) time, where λ _{7}(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7. We also show that for convex polygons, two feed-links are always sufficient and sometimes necessary to realize constant dilation, and that k feed-links lead to a dilation of 1 + O(1/k). For (α,β)-covered polygons, a constant number of feed-links suffices to realize constant dilation.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings |

Pages | 49-60 |

Number of pages | 12 |

Volume | 5664 LNCS |

DOIs | |

State | Published - 2009 |

Event | 11th International Symposium on Algorithms and Data Structures, WADS 2009 - Banff, AB, Canada Duration: Aug 21 2009 → Aug 23 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5664 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 11th International Symposium on Algorithms and Data Structures, WADS 2009 |
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Country | Canada |

City | Banff, AB |

Period | 8/21/09 → 8/23/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings*(Vol. 5664 LNCS, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5664 LNCS). https://doi.org/10.1007/978-3-642-03367-4_5

**Connect the dot : Computing feed-links with minimum dilation.** / Aronov, Boris; Buchin, Kevin; Buchin, Maike; Van Kreveld, Marc; Löffler, Maarten; Luo, Jun; Silveira, Rodrigo I.; Speckmann, Bettina.

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

*Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings.*vol. 5664 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5664 LNCS, pp. 49-60, 11th International Symposium on Algorithms and Data Structures, WADS 2009, Banff, AB, Canada, 8/21/09. https://doi.org/10.1007/978-3-642-03367-4_5

}

TY - GEN

T1 - Connect the dot

T2 - Computing feed-links with minimum dilation

AU - Aronov, Boris

AU - Buchin, Kevin

AU - Buchin, Maike

AU - Van Kreveld, Marc

AU - Löffler, Maarten

AU - Luo, Jun

AU - Silveira, Rodrigo I.

AU - Speckmann, Bettina

PY - 2009

Y1 - 2009

N2 - A feed-link is an artificial connection from a given location p to a real-world network. It is most commonly added to an incomplete network to improve the results of network analysis, by making p part of the network. The feed-link has to be "reasonable", hence we use the concept of dilation to determine the quality of a connection. We consider the following abstract problem: Given a simple polygon P with n vertices and a point p inside, determine a point q on P such that adding a feedlink minimizes the maximum dilation of any point on P. Here the dilation of a point r on P is the ratio of the shortest route from r over P and to p, to the Euclidean distance from r to p. We solve this problem in O(λ 7(n)logn) time, where λ 7(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7. We also show that for convex polygons, two feed-links are always sufficient and sometimes necessary to realize constant dilation, and that k feed-links lead to a dilation of 1 + O(1/k). For (α,β)-covered polygons, a constant number of feed-links suffices to realize constant dilation.

AB - A feed-link is an artificial connection from a given location p to a real-world network. It is most commonly added to an incomplete network to improve the results of network analysis, by making p part of the network. The feed-link has to be "reasonable", hence we use the concept of dilation to determine the quality of a connection. We consider the following abstract problem: Given a simple polygon P with n vertices and a point p inside, determine a point q on P such that adding a feedlink minimizes the maximum dilation of any point on P. Here the dilation of a point r on P is the ratio of the shortest route from r over P and to p, to the Euclidean distance from r to p. We solve this problem in O(λ 7(n)logn) time, where λ 7(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7. We also show that for convex polygons, two feed-links are always sufficient and sometimes necessary to realize constant dilation, and that k feed-links lead to a dilation of 1 + O(1/k). For (α,β)-covered polygons, a constant number of feed-links suffices to realize constant dilation.

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UR - http://www.scopus.com/inward/citedby.url?scp=69949190087&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03367-4_5

DO - 10.1007/978-3-642-03367-4_5

M3 - Conference contribution

SN - 3642033660

SN - 9783642033667

VL - 5664 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 49

EP - 60

BT - Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings

ER -