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Succinct Oracles for Exact Distances in Undirected Unweighted Graphs

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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    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
    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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