The Poset Cover Problem
نویسندگان
چکیده
A partial order or poset , P X on a (finite) base set X determines the set P of linear extensions of P . The problem of computing, for a poset P , the cardinality of P is #P-complete. A set 1 2 , , , k P P P of posets on X covers the set of linear orders that is the union of the i P . Given linear orders 1 2 , , , m L L L on X , the Poset Cover problem is to determine the smallest number of posets that cover 1 2 , , , m L L L . Here, we show that the decision version of this problem is NP-complete. On the positive side, we explore the use of cover relations for finding posets that cover a set of linear orders and present a polynomial-time algorithm to find a partial poset cover.
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