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3 Informatyka Teoretyczna i Stosowana

3 Grishkevich A.A.

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Algorytm przeliczania dwuelementowych minimalnych przekrojów grafa skierowanego

Grishkevich A.A.

Informatyka Teoretyczna i Stosowana

2006

R. 6, nr 10

85-100

Zaproponowano sposób kodowania kraty dystrybutywnej minimalnych przekrojów grafu. Opracowano algorytm przeliczania minimalnych dwuelementowych przekrojów grafu w kracie dystrybutywnej minimalnych przekrojów. Zaprezentowano przykład działania algorytmu.

Coding of the distributive lattice of the minimal cuts graphs is offered. Enumerating algorithm of the minimal two-element cuts of the graph in a distributive lattice of the minimal cuts is developed. The example of work of the algorithm is presented.

Distributive lattices in the problems of structural analysis for complex systems

Grishkevich A.A.

Informatyka Teoretyczna i Stosowana

2005

R. 5, nr 8

19-27

The problem of estimating structural reliability of complex systems is considered, the model of these systems being represented as a graph of a network type. The structural reliability is understood as the reliability component conditioned by the structure of a system, i.e. by the composition of its elements and their interconnection, the quantitative calculation of the operation particularities of functioning of the elements being not taken into account. A breach connection between the two marked vertices (source and sink) is considered as the criterion of the system's failure. In mathematical terms the solution to this problem is formulated as the problem of finding cuts (minimum cuts) of a graph separating the twa marked vertices (source, sink). Lattice-theory properties of the minimum cuts allowing to achieve an effective method for their search and enumeration are considered.

Distributive lattice of minimum cut sets of a directed graph

Grishkevich A.A.

Informatyka Teoretyczna i Stosowana

2004

R. 4, nr 7

7-22

The algebraic operations above cut sets of a digraph are entered. Is demonstrated, that the set of minimum cut sets separating two vertices of the graph, bas structure of a distributive lattice. The concept of a undecomposable (nonreducible) cut set is reviewed and the representation of set of minimum cut sets is obtained on the basis of a subset of undecomposable cut sets. The special collections of cut sets are established, in which one the nonreducible cut set is extreme. The obtained results are illustrated by example.