Theoretical and practical results in the application of algebraic structures to network reliability analysis are presented briefly. The first chapter is a quick introduction to a variety of models (deterministic and probabilistic) and performance measures for assessing the reliability of networks. In the second chapter, for a particular model (directed network, two-terminal reliability measure R _st ( G ) ), various approaches are presented for calculating network reliability (state-space enumeration, inclusion-exclusion, disjoint products, and factoring), and computational aspects are mentioned.

The third chapter develops an algebraic structure that forms a distribution lattice and is appropriate to calculate the two-terminal reliability polynomial R _st ( x ). Shier also presents the list-directed iterative algorithm and the first test network due to Satyanarayana and Prabhakar.

The fourth chapter is dedicated to the approximation of network reliability. It gives methods for bounding the two-terminal reliability of a network (lower and upper bounds and algebraic bounds). The fifth chapter presents various algebraic methods for enumerating the s-t path (depth-first search DFS(i), DFSALL(i), and Gauss-Jordan), or the s-t cutsets in a directed network.

The sixth chapter introduces the concept of an underlying semilattice, which permits the development of a pseudopolynomial recursive algorithm for calculating reliability, and presents the technique of Möbius inversion. The seventh chapter is dedicated to the reliability covering problems and provides algorithms for undirected and directed trees that are polynomially solvable. The eighth chapter investigates the state-space enumeration method based on an algebraic structure, a distributive lattice, for generating the states of a binary system, in order of nonincreasing probability, and the state-space approximation approach for multistate systems.

Every chapter has illustrative examples, and the mathematical background is minimal, so the book can be used by everyone interested in network reliability. The presentation is coherent. The book may be too short, but the bibliographical references are fine and the index is suitable.