Related papers: Rough sets and matroidal contraction
A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms…
The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially…
Contraction$^*$-depth is considered to be one of the analogues of graph tree-depth in the matroid setting. In this paper, we investigate structural properties of contraction$^*$-depth of matroids representable over finite fields and…
Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, oriented matroids, and regular matroids. To do this, we first introduce algebraic objects called tracts which…
Thin sums matroids were introduced to extend the notion of representability to non-finitary matroids. We give a new criterion for testing when the thin sums construction gives a matroid. We show that thin sums matroids over thin families…
Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…
We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined…
Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
Attribute reduction is viewed as an important preprocessing step for pattern recognition and data mining. Most of researches are focused on attribute reduction by using rough sets. Recently, Tsang et al. discussed attribute reduction with…
Matroids are a fundamental object of study in combinatorial optimization. Three closely related and important problems involving matroids are maximizing the size of the union of $k$ independent sets (that is, $k$-fold matroid union),…
Homogeneous matroids are characterized by the property that strength equals fractional arboricity, and arise in the study of base modulus [22]. For graphic matroids, Cunningham [9] provided efficient algorithms for calculating graph…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…
Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity…