http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find tree-decompositions, algorithms that use tree-decompositions to solve hard problems efficiently, graph minor theory, and some applications. The paper contains an extensive bibliography.

A tourist guide through treewidth

This paper presents an overview of results related to the computational complexity of network reliability analysis problems Network reliability analysis problems deal with the determination of reliability measures for stochastic networks We show how these problems are related to the more familiar computational network problems of recognizing certain subnetworks, finding optimal subnetworks, and counting certain subnetworks We use these relationships to show that the k-terminal, the 2-terminal, and the all-terminal network reliability analysis problems are at least as hard as the renowned set of computationally difficult problems, NP-Complete Finally, we discuss the impact of these results on how one should approach problem solving in this area

Computational Complexity of Network Reliability Analysis: An Overview

This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed.

Treewidth: Algorithmic techniques and results

Treewidth: Algorithmoc Techniques and Results

The purpose of this article is to introduce several results concerning the analysis and synthesis of reliable or invulnerable networks. First, the notion of signed reliability domination of systems is described and some applications to reliability analysis are reviewed. Then the analysis problem is considered and a brief summary of the difficulty of calculating various reliability measures is presented. Some relevant concepts in the synthesis of a most reliable network are studied. The article concludes with an introduction to a non-probabilistic approach to evaluate the vulnerability of a network. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

A survey of some network reliability analysis and synthesis results

This paper studies the problem of computing the source-to-terminal reliability, the probability that a source s can communicate with a terminal t, in a probabilistic directed network. It introduces a set of reliability-preserving reductions, called 2-neighbor-node reductions. We show that for a class of directed networks, called BSP-digraphs, such reductions are always admissible and the source-to-terminal reliability can be computed in time linear in the size of the network. A directed network D = (V, E) is a BSP-digraph if its underlying undirected graph is series-parallel. The BSP-digraphs considered can be cyclic or acyclic and both vertices as well as edges can fail. Any two vertices can be chosen as s and t. Previously, no polynomial time algorithms were known for this class of digraphs. The proposed method is also applicable to mixed graphs containing directed and undirected edges.

An O(|E|) Time Algorithm for Computing the Reliability of a Class of Directed Networks

We survey some recent polynomial-time algorithms for the exact computation of network reliability. The algorithms apply to several classes of planar networks, which include series-parallel, inner-cycle-free, inner-four-cycle-free and planar cube-free. We describe these classes and discuss the related polynomial algorithms for computing their reliability.

Efficient algorithms for reliability analysis of planar networks - a survey

A k-tree is defined recursively as follows: The complete graph Kk on k points is a k-tree. Given a k-tree G on n ≤ k points, a k-tree on n + 1 points is obtained by adding a new point u and edges connecting u to every point of a Kk in G. A graph is a partial k-tree if it is a subgraph of some k-tree. In this paper, we establish some interesting properties of partial 3-trees and show that a graph is a partial 3-tree if and only if it has no subgraph contractible to K5, K2.2.2C8(1, 4), or K2 ≤ C5. A graph G is said to be contractible to a graph H if H can be obtained from G by a sequence of edge contractions. hitherto, such a characterization of partial k-trees was known only for the values of k ≤ 2.

A characterization of partial 3-trees

This paper considers a probabilistic graph in which the points are perfectly reliable but the edges operate independently of one another, all with some known probability p. The graph G is in an operating state if the surviving edges induce a spanning connected subgraph of G. The all-terminal reliability R(G,p) of G is the probability that G is in an operating state. A graph transformation, called “the swing surgery,” is introduced, and it is shown that this surgery has important properties. First, if H is the graph obtained by deleting m independent edges from the complete graph, then for any other graph G with the same number of points and edges as H, R(H,p) > R(G,p) for all 0 < p < 1. Moreover, the swing surgery yields a simple topological proof of the well-known result that H has more spanning trees than does G. Another important consequence is that given any graph G there exists a threshold graph T with the same number of points and edges as G such that R(T,p) ≤ R(G,p) for all 0 < p < 1.

A. Satyanarayana

Papers

A survey of some network reliability analysis and synthesis results

An O(|E|) Time Algorithm for Computing the Reliability of a Class of Directed Networks

Efficient algorithms for reliability analysis of planar networks - a survey

A characterization of partial 3-trees

A reliability‐improving graph transformation with applications to network reliability