Block decomposition approach to compute a minimum geodetic set

Distinct edge geodetic decomposition in graphs

Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

Comments on “Problem Decomposition Method to Compute an Optimal Cover for a Set of Functional Dependencies”

Maier, in his seminal paper [1], presents that the problem of finding an optimal cover is NP-complete. Cotelea’s paper [2] proposes a problem decomposition method for finding an optimal cover. The basic idea of the method is: (1) a big and intractable problem (optimal cover problem) is broken down into some smaller problems; (2) particular solutions of these smaller problems are combined to con...

Problem Decomposition Method to Compute an Optimal Cover for a Set of Functional Dependencies

The paper proposes a problem decomposition method for building optimal cover for a set of functional dependencies to decrease the solving time. At the beginning, the paper includes an overview of the covers of functional dependencies. There are considered definitions and properties of non redundant covers for sets of functional dependencies, reduced and canonical covers as well as equivalence c...

A minimum data set for chronic venous disease

A sufficient condition to polynomially compute a minimum separating DFA

The computation of a minimal separating automaton (MSA) for regular languages has been studied from many different points of view, from synthesis of automata or Grammatical Inference to the minimization of incompletely specified machines or Compositional Verification. In the general case, the problem is NP-complete, but this drawback does not prevent the problem from having a real application i...