Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

• Main Authors: Thomas J. Marlowe, Laura Schoppmann
• Format: Article
• Language: English
• Published: Hindawi Limited 1998-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Computational complexity; efficient recursive algorithms; networks; reliability; threshold graphs; Gilbert's formula; graphs; polynomial-time computations.
• Online Access: http://dx.doi.org/10.1155/S1024123X98000817

Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!). We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants.