Contiguity Orders
نویسندگان
چکیده
This paper is devoted to the study of contiguity orders i.e. orders having a linear extension L such that all upper (or lower) cover sets are intervals of L. This new class is a strict generalization of both interval orders and N{free orders, and is linearly recognizable. It is proved that computing the number of contiguity extensions is #P{complete, and that the dimension of height one contiguity orders is polynomially tractable. Moreover the membership is a comparability invariant on bi{contiguity orders. Finally for strong{contiguity orders the calculation of the dimension is NP{complete. Ordres de contigu t e R esum e : Nous d eenissons les ordres de contigu t e comme poss edant une extension lin eaire pour laquelle chaque ensemble de successeurs directs appara^ t comme un intervalle. Nous etudions cette nouvelle classe d'ordres dont la reconnaissance est lin eaire, ainsi que certaines restrictions. Cette classe contient en particulier les ordres d'intervalles et les ordres sans "N", ce qui entra^ ne la NP{compl etude de la dimension et du nombre de sauts. Nous montrons que le calcul du nombre d'extensions de contigu t e est #P{complet. Concernant les ordres de contigu t e de hauteur un, nous prouvons que la dimension est un probl eme polynomial. Nous etablissons egalement l'invariance de compa-rabilit e de l'appartenance a la classe des ordres de bi{contigu t e ainsi que la NP{compl etude de la dimension pour les ordres de forte contigu t e.
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