In practical situations, there are many dynamic covering information systems with variations of attributes, but there are few studies on related family-based attribute reduction of dynamic covering information systems. In this paper, we first investigate updated mechanisms of constructing attribute reducts for consistent and inconsistent covering information systems when varying attribute sets ...

We show algorithms for computing representative families matroid intersections and use them in fixed-parameter set packing, covering, facility location problems with multiple constraints. complement our tractability results by hardness results.

Given t families, each family consisting of s finite sets, we show that if the families “separate points" in a natural way, and if the union of all the sets in all the families contains more than (s+1)t st 1 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is st st 1. Both of these bounds are best possible. This work extends rec...

Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R3 . It is shown that the unknot with maximal Thurston–Bennequin invariant of −1 has a unique linear-quadratic at infinity generating family, up to fiber-preserving diffeomorphism and stabilization. From this, invariant generating family polynomials are constructed for 2–component Legendrian links w...

On the way of generalizing recent results by Cock and the second author, it is shown that when the basis q is odd, BCH codes can be lengthened to obtain new codes with covering radius R = 2. These constructions (together with a lengthening construction by the first author) give new infinite families of linear covering codes with codimension r = 2k + 1 (the case q = 3, r = 4k + 1 was considered ...

We discuss the maximum size of uniform intersecting families with covering number at least . Among others, we construct a large k-uniform intersecting family with covering number k, which provides a counterexample to a conjecture of Lov asz. The construction for odd k can be visualized on an annulus, while for even k on a Mobius band.