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ICALP

2011

Springer

2011

Springer

Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build space-eﬃcient encodings (oracles) to perform various queries eﬃciently. We assume the word RAM model where the size of a word is Ω (log n) bits. The ﬁrst oracle, we present, is the navigation oracle which facilitates primitive navigation operations of adjacency, neighborhood, and degree queries. By way of an enumerate argument, which is of independent interest, we show the space requirement of the oracle is optimal to within lower order terms for all treewidths. The oracle supports the mentioned queries all in constant worst-case time. The second oracle, we present, is an exact distance oracle which facilitates distance queries between any pair of vertices (i.e., an all-pair shortest-path oracle). The space requirement of the oracle is also optimal to within lower order terms. Moreover, the distanc...

Added |
29 Aug 2011 |

Updated |
29 Aug 2011 |

Type |
Journal |

Year |
2011 |

Where |
ICALP |

Authors |
Arash Farzan, Shahin Kamali |

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