Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data structure in data mining and covering-based rough sets provide a systematic approach to this type of data. In this paper, we study the connectedness of graphs through covering-based rough sets a...

in recent years, in iran and other countries the power systems are going to move toward creating a competition structure for selling and buying electrical energy. these changes and the numerous advantages of dgs have made more incentives to use these kinds of generators than before. therefore, it is necessary to study all aspects of dgs, such as size selection and optimal placement and impact o...

In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable: if we choose to accept an element when it is presented by the stream then we can never get ri...

The independent sets of an algebraic matroid are sets of algebraically independent transcendentals over a field k. If a matroid M is isomorphic to an algebraic matroid the latter is called an algebraic representation of M. Vector representations of matroids are defined similarly. A matroid may have algebraic (resp. vector) representations over fields of different characteristics. The problem in...

Let H = (V, E) be a hypergraph and let k ≥ 1 and l ≥ 0 be fixed integers. LetM be the matroid with ground-set E s.t. a set F ⊆ E is independent if and only if each X ⊆ V with k|X| − l ≥ 0 spans at most k|X| − l hyperedges of F . We prove that if H is dense enough, thenM satisfies the double circuit property, thus the min-max formula of Dress and Lovász on the maximum matroid matching holds forM...

Submodular functions arewell-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions, which we call weakly submodular functions. Our extension is somewhat unusual in that it includes some (mildly) supermodular functions. We show that several natura...

Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomialtime algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial O(n) time brute force algorithm for finding a k-element sol...

This thesis is motivated by the following question: how many elements can a simple binary matroid with no PG(t, 2)-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed classes. We will answer this question by finding the eventual growth rate function of the class of matroids with no PG(t, 2)-minor, for any t ≥ 2. Our main tool will be the matroid...