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Fast lattice browsing on sparse representation

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Orders, Algorithms, and Applications (ORDAL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 831))

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Abstract

In this paper, we present an implicit data structure for partial lattices representation, which allows to efficiently perform, with respect to either time and space, the following operations: 1) testing partial order relation among two given elements and 2) given the Hasse diagram representation and two related elements u and v, returning a sequence <u 1 ,..., u l > of elements such that u ≺u 1 ≺... ≺u l ≺v. This first operation can be performed in constant time while the second in time O(l), where l is the sequence size. The data structure proposed has an overall O(n√n)-space complexity which we will prove to be optimal in the worst case. Hence, we derive an overall O(n√n)-space time bound for the relation testing problem so beating the O(n 2) bottle-neck representing the present complexity.

The overall pre-processing time is O(n 2).

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma ”La Sapienza”, Via Salaria 113, I-00198, Rome, Italy

    Maurizio Talamo

  2. Dipartimento di Matematica, Università di Roma ”Tor Vergata”, Via della Ricerca Scientifica, I-00173, Rome, Italy

    Paola Vocca

Authors
  1. Maurizio Talamo
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  2. Paola Vocca
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Editor information

Vincent Bouchitté Michel Morvan

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© 1994 Springer-Verlag Berlin Heidelberg

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Talamo, M., Vocca, P. (1994). Fast lattice browsing on sparse representation. In: Bouchitté, V., Morvan, M. (eds) Orders, Algorithms, and Applications. ORDAL 1994. Lecture Notes in Computer Science, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019435

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  • DOI: https://doi.org/10.1007/BFb0019435

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58274-8

  • Online ISBN: 978-3-540-48597-1

  • eBook Packages: Springer Book Archive

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