J.P. Bordat. Calcul des ideaux d'un ordonne ni. Recherche Operationnelle / Operations Research, 25(4):265-275, 1991.  Home/Search   Document Not in Database   Summary   Related Articles

....compute D or G from H is not linear in the general case, see [1] From the original de nition of distributive lattices, one can produce a naive recognition algorithm running in O(n 3 ) when the input is a covering graph D = X; E tr ) with jXj = n. Under the same assumption, recently Bordat [5] has proposed an O(jE tr jloglog ) algorithm based upon traversals of directed graphs, where is the maximal out degree of the input graph which is a covering graph. When the input is any graph whose transitive closure is the lattice, Bordat s algorithm turns out to be in O(n 2 ) We present ....

.... main result emphasizes the algorithmic applications of a well known representation theorem for distributive lattices [3, 4, 8] We also use part of the knowledge on algorithmic order theory slowly gathered on basic problems such as transitive (closure and reduction) calculations on acyclic graphs [5, 12, 10]. These results show in that example of distributive lattices that ecient algorithms are closely related to structural properties. This approach can be generalized to other classes of orders. An order P is said to be graded if all maximal chains between any two elements of P have the same length. ....

J.P. Bordat. Calcul des ideaux d'un ordonne ni. Recherche Operationnelle / Operations Research, 25(4):265-275, 1991.

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