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FOCS

2009

IEEE

2009

IEEE

Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efﬁcient algorithm to construct an approximate distance oracle using space O(kn1+1/k ) that can answer queries in time O(k) with a distance estimate that is at most α = 2k − 1 times larger than the actual shortest distance (α is called the stretch). They proved that, under a combinatorial conjecture, their data structure is optimal in terms of space: if a stretch of at most 2k−1 is desired, then the space complexity is at least n1+1/k . Their proof holds even if inﬁnite query time is allowed: it is essentially an “incompressibility” result. Also, the proof only holds for dense graphs, and the best bound it can prove only implies that the size of the data structure is lower bounded by the number of edges of the graph. Naturally, the following question arises: what happens for s...

Related Content

Added |
20 May 2010 |

Updated |
20 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
FOCS |

Authors |
Christian Sommer 0002, Elad Verbin, Wei Yu |

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