Related papers: Correspondence Between Two Antimatroid Algorithmic…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
We generalize the 1/3-2/3 conjecture from partially ordered sets to antimatroids: we conjecture that any antimatroid has a pair of elements x,y such that x has probability between 1/3 and 2/3 of appearing earlier than y in a uniformly…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
We construct a family of independent sets for finite, atomic, and graded lattices, extending the well-known cryptomorphism between geometric lattices and matroids. This construction leads to an embedding theorem into geometric lattices that…
In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-analogue of a matroid where subspaces play the role of the…
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
This paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why they are (not) cryptomorphic. Also, we explain the…
We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary…
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)…
This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be…
Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We explore novel connections between antimatroids and matchings in bipartite graphs. In particular, we prove that a combinatorial structure induced by stable matchings or maximum-weight matchings is an antimatroid. Moreover, we demonstrate…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
Let $M$ be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and $min\{r(L), r^*(E\backslash L)\} \geq 2$. Locked subsets characterize nontrivial facets of the…
The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a…
Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with…