Dimension schemas are abstract models of the data hierarchies that populate OLAP warehouses. Although there is abundant work on schema equivalence in a variety of data models, these works do not cover dimension schemas. In this paper we propose a notion of equivalence that allows to compare dimension schemas with respect to their information capacity. The proposed notion is intended to capture ...

One of the most common ways of representing classes of equivalent Bayesian networks is the use of essential graphs. These chain graphs are also known in the literature as completed patterns or completed pdags. The name essential graph was proposed by Andersson, Madigan and Perlman (1997a) who also gave a graphical characterization of essential graphs. In this contribution an alternative charact...

Given a graph G, a vertex switch of v ∈ V (G) results in a new graph where neighbors of v become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on n vertices. The equivalence class of G with respect to the switching operation is commonly referred to as G’s switching class. The algebraic and combinatorial properties of switching...

Two words u and v are k-abelian equivalent if for each word x of length at most k, x occurs equally many times as a factor in both u and v. The notion of k-abelian equivalence is an intermediate notion between the abelian equivalence and the equality of words. In this paper, we study the equivalence classes induced by the k-abelian equivalence, mainly focusing on the cardinalities of the classe...

Garnero et al. [SIAM J. Discrete Math. 2015, 29(4):1864–1894] recently introduced a framework based on dynamic programming to make applications of the protrusion replacement technique constructive and to obtain explicit upper bounds on the involved constants. They show that for several graph problems, for every boundary size t one can find an explicit setRt of representatives. Any subgraph H wi...

Today, the computational complexity of equivalence problems such as the graph isomorphism problem and the Boolean formula equivalence problem remain only partially understood. One of the most important tools for determining the (relative) difficulty of a computational problem is the many-one reduction, which provides a way to encode an instance of one problem into an instance of another. In equ...