Ferragina, Paolo and Nitto, Igor and Venturini, Rossano (2007) *Succinct Oracles for Exact Distances in Undirected Unweighted Graphs.* Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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## Abstract

Let G be an unweighted and undirected graph of n nodes, and let D be the n x n matrix storing the All-Pairs-Shortest-Path distances in G. Since D contains integers in [n], its plain storage takes n^2log (n + 1) bits. However, a simple counting argument shows that n^2/2 bits are necessary to store D. In this paper we investigate the question of finding a succinct representation of D that requires O(n^2) bits of storage and still supports constant-time access to each of its entries. This is asymptotically optimal in the worst case, and far from the information-theoretic lower-bound by a multiplicative factor log 3 \simeq 1.585. As a result O(1) bits per pairs of nodes in G are enough to retain constant-time access to their shortest-path distance. We achieve this result by reducing the storage of D to the succinct storage of labeled trees and ternary sequences, for which we properly adapt and orchestrate the use of known compressed data structures.

Item Type: | Book |
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Uncontrolled Keywords: | All-Pairs-Shortest-Path distances, Compressed indexes for strings and trees, Distance oracles for graphs, Succinct Data Structures |

Subjects: | Area01 - Scienze matematiche e informatiche > INF/01 - Informatica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA |

Depositing User: | dott.ssa Sandra Faita |

Date Deposited: | 09 Dec 2014 13:16 |

Last Modified: | 09 Dec 2014 13:16 |

URI: | http://eprints.adm.unipi.it/id/eprint/2184 |

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