# Publications

This paper describes *BBMCW*, a new efficient exact maximum clique algorithm tailored for large sparse graphs which can be bit-encoded directly into memory without a heavy performance penalty. These graphs occur in real-life problems when some form of locality may be exploited to reduce their scale. One such example is correspondence graphs derived from data association problems. The new algorithm is based on the bit-parallel kernel used by the *BBMC* family of published exact algorithms. *BBMCW* employs a new bitstring encoding that we denote ‘watched’, because it is reminiscent of the ‘watched literal’ technique used in satisfiability and other constraint problems. The new encoding reduces the number of spurious operations computed by the *BBMC* bit-parallel kernel in large sparse graphs. Moreover, *BBMCW* also improves on bound computation proposed in the literature for bit-parallel solvers. Experimental results show that the new algorithm performs better than prior algorithms over data sets of both real and synthetic sparse graphs. In the real data sets, the improvement in performance averages more than two orders of magnitude with respect to the state-of-the-art exact solver *IncMaxCLQ*.

Flow variations over time generalize standard network flows by introducing an element of time. In contrast to the classical case of static flows, a flow over time in such a network specifies a flow rate entering an arc for each point in time. In this setting, the capacity of an arc limits the rate of flow into the arc at each point in time. Traditionally, flows over time are computed in time-expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static network flows, its drawback is the enormous size of the time-expanded network. In this paper, we extend the results about the minimum flow problem to network flows (with n nodes and m arcs) in which the time-varying lower bounds can involve both the source and the sink nodes (as in Fathabadi et al.) and also one additional node other than the source and the sink nodes. It is shown that this problem for the set (Formula presented.) of time points can be solved by at most n minimum flow computations, by suitably extending the dynamic minimum flow algorithm and reoptimization techniques. The running time of the presented algorithm is (Formula presented.).

In this paper we examine the maintenance decision support in classification of the dangerous situations discovered by the monitoring system. This task is reduced to the contextual multi-armed bandit problem. We highlight small sample size problem appeared in this task due to the rather rare failures. The novel algorithm based on the nearest neighbor search is proposed. An experimental study is provided for several synthetic datasets with the situations described by either simple features or grayscale images. It is shown, that our algorithm outperforms the well-known contextual multi-armed methods with the Upper Confidence Bound and softmax random search strategies.

This paper addresses the problem of insufficient performance of statistical classification with the medium-sized database (thousands of classes). Each object is represented as a sequence of independent segments. Each segment is defined as a random sample of independent features with the distribution of multivariate exponential type. To increase the speed of the optimal Kullback-Leibler minimum information discrimination principle, we apply the clustering of the training set and an approximate nearest neighbor search of the input object in a set of cluster medoids. By using the asymptotic properties of the Kullback-Leibler divergence, we propose the maximal likelihood search procedure. In this method the medoid to check is selected from the cluster with the maximal joint density (likelihood) of the distances to the previously checked medoids. Experimental results in image recognition with artificially generated dataset and Essex facial database prove that the proposed approach is much more effective, than an exhaustive search and the known approximate nearest neighbor methods from FLANN and NonMetricSpace libraries.

A class of graphs is called monotone if it is closed under deletion of vertices and edges. Any such class may be defined in terms of forbidden subgraphs. The chromatic index of a graph is the smallest number of colors required for its edge-coloring such that any two adjacent edges have different colors. We obtain a complete classification of the complexity of the chromatic index problem for all monotone classes defined in terms of forbidden subgraphs having at most 6 edges or at most 7 vertices.

The notions of boundary and minimal hard classes of graphs, united by the term “critical classes”, are useful tools for analysis of computational complexity of graph problems in the family of hereditary graph classes. In this family, boundary classes are known for several graph problems. In the paper, we consider critical graph classes in the families of strongly hereditary and minor closed graph classes. Prior to our study, there was the only one example of a graph problem for which boundary classes were completely described in the family of strongly hereditary classes. Moreover, no boundary classes were known for any graph problem in the family of minor closed classes. In this article, we present several complete descriptions of boundary classes for these two families and some classical graph problems. For the problem of 2-additive approximation of graph bandwidth, we find a boundary class in the family of minor closed classes. Critical classes are not known for this problem in the other two families of graph classes.

In this paper we focus on two essential problems of maintenance decision support systems, namely, 1) detection of potential dangerous situation, and 2) classification of this situation in order to recommend an appropriate repair action. The former task is usually solved with the known statistical process control techniques. The latter problem can be reduced to the contextual multi-armed bandit problem. We propose a novel algorithm with Bayesian classification of abnormal situation and the softmax rule to explore the decision space. The dangerous situations are detected with the Shewhart control charts for the distances between the current and the normal situations. It is experimentally shown, that our algorithm is more accurate than the known contextual multi-armed methods with stochastic search strategies.

Deep convolutional neural networks are widely used to extract high-dimensional features in various image recognition tasks. If the count of classes is relatively large, performance of the classifier for such features can be insufficient to be implemented in real-time applications, e.g., in video-based recognition. In this paper we propose the novel approximate nearest neighbor algorithm, which sequentially chooses the next instance from the database, which corresponds to the maximal likelihood (joint density) of distances to previously checked instances. The Gaussian approximation of the distribution of dissimilarity measure is used to estimate this likelihood. Experimental study results in face identification with LFW and YTF datasets are presented. It is shown that the proposed algorithm is much faster than an exhaustive search and several known approximate nearest neighbor methods.

We analyzed the way to increase computational efficiency of video-based image recognition methods with matching of high dimensional feature vectors extracted by deep convolutional neural networks. We proposed an algorithm for approximate nearest neighbor search. At the first step, for a given video frame the algorithm verifies a reference image obtained when recognizing the previous frame. After that the frame is compared with a few number of reference images. Each next examined reference image is chosen so that to maximize conditional probability density of distances to the reference instances tested at previous steps. To decrease the required memory space we beforehand calculate only distances from all the images to small number of instances (pivots). When experimenting with either face photos from Labeled Faces in the Wild and PubFig83 datasets or with video data from YouTube Faces we showed that our algorithm allows accelerating the recognition procedure by 1.4–4 times comparing with known approximate nearest neighbor methods.

Given a graph, the Edge minimum sum-of-squares clustering problem requires finding *p* prototypes (cluster centres) by minimizing the sum of their squared distances from a set of vertices to their nearest prototype, where a prototype can be either a vertex or an inner point of an edge. In this paper we have implemented Variable neighborhood search based heuristic for solving it. We consider three different local search procedures, K-means, J-means, and a new I-means heuristic. Experimental results indicate that the implemented VNS-based heuristic produces the best known results in the literature.

An exhaustive search of all classes in pattern recognition methods cannot be implemented in real-time, if the database contains a large number of classes. In this paper we introduce a novel probabilistic approximate nearest-neighbor (NN) method. Despite the most of known fast approximate NN algorithms, our method is not heuristic. The joint probabilistic densities (likelihoods) of the distances to previously checked reference objects are estimated for each class. The next reference instance is selected from the class with the maximal likelihood. To deal with the quadratic memory requirement of this approach, we propose its modification, which processes the distances from all instances to a small set of pivots chosen with the farthest-first traversal. Experimental study in face recognition with the histograms of oriented gradients and the deep neural network-based image features shows that the proposed method is much faster than the known approximate NN algorithms for medium databases.

This valuable source for graduate students and researchers provides a comprehensive introduction to current theories and applications in optimization methods and network models. Contributions to this book are focused on new efficient algorithms and rigorous mathematical theories, which can be used to optimize and analyze mathematical graph structures with massive size and high density induced by natural or artificial complex networks. Applications to social networks, power transmission grids, telecommunication networks, stock market networks, and human brain networks are presented.

Chapters in this book cover the following topics:

Linear max min fairness Heuristic approaches for high-quality solutions Efficient approaches for complex multi-criteria optimization problems Comparison of heuristic algorithms New heuristic iterative local search Power in network structures Clustering nodes in random graphs Power transmission grid structure Network decomposition problems Homogeneity hypothesis testing Network analysis of international migration Social networks with node attributes Testing hypothesis on degree distribution in the market graphs Machine learning applications to human brain network studies

This proceeding is a result of The 6th International Conference on Network Analysis held at the Higher School of Economics, Nizhny Novgorod in May 2016. The conference brought together scientists and engineers from industry, government, and academia to discuss the links between network analysis and a variety of fields.

Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a new class of statistical procedures for market graph identification was introduced and the optimality of these procedures in the Pearson correlation Gaussian network was proved. However, the procedures obtained have a high reliability only for Gaussian multivariate distributions of stock attributes. One of the ways to correct this problem is to consider different networks generated by different measures of pairwise similarity of stocks. A new and promising model in this context is the sign similarity network. In this paper the market graph identification problem in the sign similarity network is reviewed. A new class of statistical procedures for the market graph identification is introduced and the optimality of these procedures is proved. Numerical experiments reveal an essential difference in the quality between optimal procedures in sign similarity and Pearson correlation networks. In particular, it is observed that the quality of the optimal identification procedure in the sign similarity network is not sensitive to the assumptions on the distribution of stock attributes.

We consider the coloring problem for hereditary graph classes, i.e. classes of simple unlabeled graphs closed under deletion of vertices. For the family of the hereditary classes of graphs defined by forbidden induced subgraphs with at most four vertices, there are three classes with an open complexity of the problem. For the problem and the open three cases, we present approximation polynomial-time algorithms with performance guarantees.

The independent set problem for a given simple graph consists in computing the size of a largest subset of its pairwise nonadjacent vertices. In this article, we prove the polynomial solvability of the problem for the subcubic planar graphs with no induced tree obtained by identifying the ends of three paths of lengths 3, 3, and 2 respectively.

In recent years, as a result of the increase in environmental problems, green logistics has become a focus of interest by researchers, governments, policy makers, and investors. In this study, a cumulative multi-trip vehicle routing problem with limited duration (CumMTVRP-LD) is modelled by taking into account the reduction of CO 2 emissions. In classical vehicle routing problems (VRP), each vehicle can perform only one trip. Because of the high investment costs of additional vehicles, organizations allow the vehicles to perform multiple trips as in multi-trip vehicle routing problems (MTVRP), which reflects the real requirements better than the classical VRP. This study contributes to the literature by using a mixed integer programming (MIP) formulation and a simulated annealing (SA) based solution methodology for CumMTVRP-LD, which considers the minimization of fuel consumption as the objective function. According to preliminary computational results using benchmark problems in the literature, the proposed methodology obtained promising results in terms of solution quality and computational time.

A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in the class of elliptically contoured distributions. Moreover it is shown that these procedures can be adapted for distribution free threshold graph identification in Pearson correlation network.

In this paper it is proposed to improve performance of the automatic speech recognition by using sequential three-way decisions. At first, the largest piecewise quasi-stationary segments are detected in the speech signal. Every segment is classified using the maximum a-posteriori (MAP) method implemented with the Kullback-Leibler minimum information discrimination principle. The three-way decisions are taken for each segment using the multiple comparisons and asymptotical properties of the Kullback-Leibler divergence. If the non-commitment option is chosen for any segment, it is divided into small subparts, and the decision-making is sequentially repeated by fusing the classification results for each subpart until accept or reject options are chosen or the size of each subpart becomes relatively low. Thus, each segment is associated with a hierarchy of variable-scale subparts (granules in rough set theory). In the experimental study the proposed procedure is used in speech recognition with Russian language. It was shown that our approach makes it possible to achieve high efficiency even in the presence of high level of noise in the observed utterance.