Wyznaczanie m-optymalnych podstruktur opiniowania diagnostycznego hipersześcianu zredukowanego

Artykuł dotyczy projektowania takich m-optymalnych struktur opiniowania diagnostycznego (struktur OD) typu PMC, które są grafami częściowymi zredukowanego hipersześcianu wymiaru n. Zaproponowano metodę projektowania m-optymalnej struktury OD względem zredukowanego hipersześcianu wymiaru n, gdzie n > m, która bazuje na spójnym rdzeniu struktury m-optymalnej.

A diagnostic opinion system is such a diagnostic system which is self-diagnosable - which means that in the system there exists an algorithm capable of identifying its faulty elements. In this article, it was proposed a method of designing such m-optimal system of PMC type which is the edge-induced subgraph of reduced hypercube. A specific method is based on a special class of undirected digraphs called the core. The core is an edge-induced subgraph of an m-optimal strongly connected component obtained by deleting all directed arches. Once the core is constructed, the strongly connected component is obtained by supplementing it with missing directed arches of reduced hypercube which are not in set of core edges. In order to have m-optimal structure, the obtained graph has to exhibit the so-called Hakimi and Amin Properties.