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WADS

2007

Springer

2007

Springer

A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real number t > 1, we say that a subgraph G′ of a graph G is a t-spanner of G, if for every pair of vertices u, v in G, there exists a path in G′ of length at most t times the distance between u and v in G. In this paper, we consider the problem of efﬁciently constructing sparse spanners of ball graphs which supports fast shortest path distance queries. We present the ﬁrst algorithm for constructing spanners of ball graphs. For a ball graph in Rk, we construct a (1 + ǫ)-spanner for any ǫ > 0 with O(nǫ−k+1) edges in O(n2ℓ+δǫ−k logℓ S) time, using an efﬁcient partitioning of space into hypercubes and solving intersection problems. Here ℓ = 1 − 1/(⌊k/2⌋ + 2), δ is any positive constant, and S is the ratio between the largest and smallest radius. For the special case when the balls all have unit size, we show that the complexity of constructing a (1 + ǫ)-spanner is a...

Related Content

Added |
09 Jun 2010 |

Updated |
09 Jun 2010 |

Type |
Conference |

Year |
2007 |

Where |
WADS |

Authors |
Martin Fürer, Shiva Prasad Kasiviswanathan |

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