An Algorithm for Minimal Insertion in a Type Lattice
نویسنده
چکیده
We consider the insertion of a new element x in a lattice of types L. As the poset L + x obtained by the direct insertion of x in L, is not necessarily a lattice, a set of auxiliary elements should be added in order to restore the lattice properties. We describe an approach towards the lattice insertion based on a global deenition of the set of necessary auxiliary elements and their location in L. For that reason, the set of GLB (LUB) of elements in L superior (inferior) to x is considered. Each GLB and LUB which is incomparable with x gives rise to exactly one auxiliary element. The obtained lattice, L + , is isomorphic to the Dedekind-McNeille completion of L + x and thus it is minimal in size. In addition, the insertion strategy is more general than the existing ones, since it deals with general kind lattices and makes no hypothesis on the location of x in L. An algorithm computing L + from L and x of time complexity O(jLj!(L)(jLj + ! 2 (L))) is provided.
منابع مشابه
An Algorithm for Minimal Insertion in a Type Lattice 3
2 The problem of inserting a new element x into a lattice of types L is addressed in the paper. As the poset L + x obtained by the direct insertion of x in L, is not necessarily a lattice, some set of auxiliary elements should be added to restore the lattice properties. An approach towards the lattice insertion is presented which allows the set of auxiliary elements to be kept minimal. The key ...
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