The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

Although questions about social cohesion lie at the core of our discipline, definitions are often vague and difficult to operationalize. Here, research on social cohesion and social embeddedness is linked by developing a concept of structural cohesion based on network node connectivity. Structural cohesion is defined as the minimum number of actors who, if removed from a group, would disconnect the group. A structural dimension of embeddedness can then be defined through the hierarchical nesting of these cohesive structures. The empirical applicability of nestedness is demonstrated in two dramatically different substantive settings, and additional theoretical implications with reference to a wide array of substantive fields are discussed.

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Structural cohesion and embeddedness: A hierarchical concept of social groups

Complexity and Approximation

We present a factor 2 approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorithm first solves the linear relaxation of this problem, and then iteratively rounds off the solution. The key idea in rounding off is that in a basic solution of the LP relaxation, at least one edge gets included at least to the extent of half. We include this edge into our integral solution and solve the residual problem.

A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem

Approximation algorithms for graph augmentation

An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of an (undirected or directed) simple graph G=(V,E). There are four versions of the problem, and the approximation guarantees are as follows:
minimum-size k-node connected spanning subgraph of an undirected graph 1 + [1/k], minimum-size k-node connected spanning subgraph of a directed graph 1 + [1/k], minimum-size k-edge connected spanning subgraph of an undirected graph 1+[2/(k+1)], minimum-size k-edge connected spanning subgraph of a directed graph 1 + [4/\sqrt{k}]. 
The heuristic is based on a subroutine for the degree-constrained subgraph (b-matching) problem. It is simple and deterministic and runs in time O(k|E|2).
The following result on simple undirected graphs is used in the analysis: The number of edges required for augmenting a graph of minimum degree k to be k-edge connected is at most k,|V|/(k+1).
For undirected graphs and k=2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or 2-edge connected) spanning subgraph whose size is within a factor of ($1.5+\epsilon$) of minimum, where $\epsilon>0$ is a constant.

/pdf/approximating-minimum-size-k-connected-spanning-subgraphs-43qvqkeuny.pdf

Approximating Minimum-Size k -Connected Spanning Subgraphs via Matching

Embodiments of the present invention provide increase resiliency to server failures by migrating TCP-based connections to backup servers, thus mitigating damage from servers disabled by attacks or accidental failures. The failover mechanism described is completely transparent to the client. Using these techniques, simple, practical systems can be built that can be retrofitted into the existing infrastructure, i.e. without requiring changes either to the TCP/IP protocol, or to the client system.

Techniques for client-transparent TCP migration

The high number of false positive alarms that are generated in large intrusion detection infrastructures makes it difficult for operations staff to separate false alerts from real attacks. One means of reducing this problem is the use of meta alarms, or rules, which identify known attack patterns in alarm streams. The obvious risk with this approach is that the rule base may not be complete with respect to every true attack profile, especially those which are new. Currently, new rules are discovered manually, a process which is both costly and error prone. We present a novel approach using association rule mining to shorten the time that elapses from the appearance of a new attack profile in the data to its definition as a rule in the production monitoring infrastructure.

A framework for the application of association rule mining in large intrusion detection infrastructures

We study the problem of increasing the connectivity1 of a graph at an optimal cost. Since the general problem is NP-hard, we focus on efficient approximation schemes that come within a constant factor from the optimal. Previous algorithms either do not take edge costs into consideration, or run slower than our algorithm. Our algorithm takes as input an undirected graph G0 = (V, E0) on n vertices, that is not necessarily connected, and a set Feasible of m weighted edges on V, and outputs a subset Aug of edges which when added to G0 make it 2-connected. The weight of Aug, when G0 is initially connected, is no more than twice the weight of the least weight subset of edges of Feasible that increases the connectivity to 2. The running time of our algorithm is O(m + n logn). We also study the problem of increasing the edge connectivity of any graph G, to k, within a factor of 2 (for any k > 0). The running time of this algorithm is O(nk log n(m + n log n)). We observe that when k is odd we can use different techniques to obtain an approximation factor of 2 for increasing edge connectivity from k to (k+1) in O(kn2) time.

Ramakrishna Thurimella

Papers

Approximation algorithms for graph augmentation

Approximating Minimum-Size k -Connected Spanning Subgraphs via Matching

Techniques for client-transparent TCP migration

A framework for the application of association rule mining in large intrusion detection infrastructures

Approximation Algorithms for Graph Augmentation