Miro Kraetzl

The Cross-Entropy Method for Network Reliability Estimation

Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network—expressed as the probability that certain nodes in the network are connected—is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability estimation procedures. Three techniques of estimation are considered: Crude Monte Carlo and the more sophisticated Permutation Monte Carlo and Merge Process. We show that the Cross-Entropy method yields a speed-up over all three techniques.

Matching graphs with unique node labels

A special class of graphs is introduced in this paper. The graphs belonging to this class are characterised by the existence of unique node labels. A number of matching algorithms for graphs with unique node labels are developed. It is shown that problems such as graph isomorphism, subgraph isomorphism, maximum common subgraph (MCS) and graph edit distance (GED) have a computational complexity that is only quadratic in the number of nodes. Moreover, computing the median of a set of graphs is only linear in the cardinality of the set. In a series of experiments, it is demonstrated that the proposed algorithms run very fast in practice. The considered class makes the matching of large graphs, consisting of thousands of nodes, computationally tractable. We also discuss an application of the considered class of graphs and related matching algorithms to the classification and detection of abnormal events in computer networks.

On graphs with unique node labels

A special class of graphs is introduced in this paper. The graphs belonging to this class are characterised by the existence of unique node labels. A number of matching algorithms for graphs with unique node labels are developed. It is shown that problems such as graph isomorphism, subgraph isomorphism, maximum common subgraph and others have a computational complexity that is only quadratic in the number of nodes. We also discuss some potential applications of the considered class of graphs.

DETECTION OF ABNORMAL CHANGE IN A TIME SERIES OF GRAPHS

In the management of large enterprise communication networks, it becomes difficult to detect and identify causes of abnormal change in traffic distributions when the underlying logical topology is ...

THE TREE CUT AND MERGE ALGORITHM FOR ESTIMATION OF NETWORK RELIABILITY

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Computer network monitoring and abnormal event detection using graph matching and multidimensional scaling

Computer network monitoring and abnormal event detection have become important areas of research. In previous work, it has been proposed to represent a computer network as a time series of graphs and to compute the difference, or distance, of consecutive graphs in such a time series. Whenever the distance of two graphs exceeds a given threshold, an abnormal event is reported. In the present paper we go one step further and compute graph distances between all pairs of graphs in a time series. Given these distances, a multidimensional scaling procedure is applied that maps each graph onto a point in the two-dimensional real plane, such that the distances between the graphs are reflected, as closely as possible, in the distances between the points in the two-dimensional plane. In this way the behaviour of a network can be visualised and abnormal events as well as states or clusters of states of the network can be graphically represented. We demonstrate the feasibility of the proposed method by means of synthetically generated graph sequences and data from real computer networks.

SIMILARITY MEASURES FOR HIERARCHICAL REPRESENTATIONS OF GRAPHS WITH UNIQUE NODE LABELS

A hierarchical abstraction scheme based on node contraction and two related similarity measures for graphs with unique node labels are proposed in this paper. The contraction scheme reduces the number of nodes in a graph and leads to a speed-up in the computation of graph similarity. Theoretical properties of the new graph similarity measures are derived and experimentally verified. A potential application of the proposed graph abstraction scheme in the domain of computer network monitoring is discussed.

Theoretical and algorithmic framework for hypergraph matching

Graphs have been successfully used in many disciplines of science and engineering. In the field of pattern recognition and image analysis, graph matching has proven to be a powerful tool. In this paper we generalize various matching tasks from graphs to the case of hypergraphs. We also discuss related algorithms for hypergraph matching.

Novel approaches in modelling dynamics of networked surveillance environment

In this paper novel applications of dy- namic graphs modelling to specific problems of manage- ment of networked surveillance sensors are proposed. The applicability of behavioural analysis oj time se- ries of labelled and attributed digraphs to detection of abnormal changes, possible forecasting of anomalous events, and general performance management of net- worked sensor environments is explored.

Network reliability estimation using the tree cut and merge algorithm with importance sampling

It is well known that the exact calculation of network reliability is a NP-complete problem and that for large networks estimating the reliability using simulation techniques becomes attractive. For highly reliable networks, a Monte Carlo scheme called the Merge Process is one of the best performing algorithms, but with a relatively high computational cost per sample. The authors previously proposed a hybrid Monte Carlo scheme called the Tree Cut and Merge algorithm which can improve simulation performance by over seven orders of magnitude in some heterogeneous networks. In homogeneous networks, however, the performance of the algorithm may degrade. In this paper, we first analyse the Tree Cut and Merge algorithm and explain why it does not perform well in some networks. Then a modification is proposed that subdivides the problem into smaller problems and introduces the Importance Sampling technique to the simulation process. The modified algorithm addresses the slow convergence problem in those hard cases while keeping the performance improvement in heterogeneous networks. Experiments and results are presented with some discussions.