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Algorithms and Order pp 231–279Cite as

The Calculation of Invariants for Ordered Sets

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Part of the book series: NATO ASI Series ((ASIC,volume 255))

Abstract

In this paper we survey complexity results yielded by the calculation of untractable invariants of ordered sets dealing with the computation of linear extensions. The main invariants we consider here are the dimension, the jump number, and the number of linear extensions.

First we investigate recent NP-completeness results, and then consider some recent polynomial results on some particular recognizable polynomially classes of posets for which significant computational results are known, namely: tree-like, series-parallel, N-free, bounded width, substitution of bounded width, cycle-free, 2-dimensional, interval orders, and semi-orders. The aim of our present work is to precisely handle the borderline polynomiality / NP-completeness for these invariants. We end by listing a few conjectures that arise naturally from this survey.

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  1. Département Informatique et Réseaux, ZI de Kernevent, Ecole Nationale Supérieure des Télécommunications de Bretagne, BP 832, 29285, Brest cédex, France

    V. Bouchitte & M. Habib

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  1. V. Bouchitte
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  1. Departments of Computer Science and Mathematics, University of Ottawa, Ottawa, Canada

    Ivan Rival

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Bouchitte, V., Habib, M. (1989). The Calculation of Invariants for Ordered Sets. In: Rival, I. (eds) Algorithms and Order. NATO ASI Series, vol 255. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2639-4_6

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