An enumeration algorithm for combinatorial problems of the reliability analysis of binary coherent systems

Abstract

In this paper the problem of the generation of all elements of a system of sets is investigated and a backtrack algorithm (Al) is given solving this problem.The algorithm is applied to combinatorial problems of reliability:

A t-graph is interpreted as a binary coherent system S and the system function of S is represented as the sum of Boolean orthogonal products. This approach is a simple and efficient alternative to a method suggested by Satyanarayana and N. Hagstbom [9].

A directed p-graph is also interpreted as a binary coherent system S and both the minimal cuts of S and the cocycles of G are determined.

Keywords:

• Enumeration
• combinatorics
• reliability
• graph theory

AMS 1980 Subject Classifications:

• Primary: 05 A 15
• Secondary: 05 C 30
• Secondary: 62 N 05