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## Scalable Distributed Algorithm for Approximate Nearest Neighbor Search Problem in High Dimensional General Metric Spaces

We propose a novel approach for solving the approximate nearest neighbor search problem in arbitrary metric spaces. The distinctive feature of our approach is that we can incrementally build a non-hierarchical distributed structure for given metric space data with a logarithmic complexity scaling on the size of the structure and adjustable accuracy probabilistic nearest neighbor queries. The structure is based on a small world graph with vertices corresponding to the stored elements, edges for links between them and the greedy algorithm as base algorithm for searching. Both search and addition algorithms require only local information from the structure. The performed simulation for data in the Euclidian space shows that the structure built using the proposed algorithm has navigable small world properties with logarithmic search complexity at fixed accuracy and has weak (power law) scalability with the dimensionality of the stored data.

Given a closed interval $I=[a,b]$ and a metric space $(M,d)$, we introduce a

nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^I$ (the set of all

functions from $I$ into $M$), called the {\it joint modulus of variation}. We show that

if two sequences of functions $\{f_j\}$ and $\{g_j\}$ from $M^I$ are such that

$\{f_j\}$ is pointwise relatively compact on $I$, $\{g_j\}$ is pointwise convergent on $I$,

and $\limsup_{j\to\infty}\nu_n(f_j,g_j)=o(n)$ as $n\to\infty$, then $\{f_j\}$ admits

a pointwise convergent subsequence whose limit on $I$ is a conditionally regulated function.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

Bandwidth distributed algorithm for interface of input signal subsystem is developed. Algorithm is based on weighting coefficient method related to speeds of thread and verified in MatLab. Example of registration system and timing diagram is shown.

The notion of a modular is introduced as follows. A (metric) *modular* on a set *X* is a function *w*:(0,*∞*)×*X*×*X*→[0,*∞*] satisfying, for all *x*,*y*,*z*∈*X*, the following three properties: *x*=*y* if and only if *w*(*λ*,*x*,*y*)=0 for all *λ*>0; *w*(*λ*,*x*,*y*)=*w*(*λ*,*y*,*x*) for all *λ*>0; *w*(*λ*+*μ*,*x*,*y*)≤*w*(*λ*,*x*,*z*)+*w*(*μ*,*y*,*z*) for all *λ*,*μ*>0. We show that, given *x*0∈*X*, the set *X**w*={*x*∈*X*:lim*λ*→*∞**w*(*λ*,*x*,*x*0)=0} is a metric space with metric , called a *modular space*. The modular *w* is said to be *convex* if (*λ*,*x*,*y*)↦*λ**w*(*λ*,*x*,*y*) is also a modular on *X*. In this case *X**w* coincides with the set of all *x*∈*X* such that *w*(*λ*,*x*,*x*0)<*∞* for some *λ*=*λ*(*x*)>0 and is metrizable by . Moreover, if or , then ; otherwise, the reverse inequalities hold. We develop the theory of metric spaces, generated by modulars, and extend the results by H. Nakano, J. Musielak, W. Orlicz, Ph. Turpin and others for modulars on linear spaces.

Similarity searching has a vast range of applications in various fields of computer science. Many methods have been proposed for exact search, but they all suffer from the curse of dimensionality and are, thus, not applicable to high dimensional spaces. Approximate search methods are considerably more efficient in high dimensional spaces. Unfortunately, there are few theoretical results regarding the complexity of these methods and there are no comprehensive empirical evaluations, especially for non-metric spaces. To fill this gap, we present an empirical analysis of data structures for approximate nearest neighbor search in high dimensional spaces. We provide a comparison with recently published algorithms on several data sets. Our results show that small world approaches provide some of the best tradeoffs between efficiency and effectiveness in both metric and non-metric spaces.

This volume contains the papers presented at the 6th International Conference on Similarity Search and Applications (SISAP 2013), held at A Coruna, Spain, during October 2–4, 2013. The International Conference on Similarity Search and Applications (SISAP) is an annual forum for researchers and application developers in the area of similarity data management. It aims at the technological problems shared by many application domains, such as data mining, information retrieval, computer vision, pattern recognition, computational biology, geography, biometrics, machine learning, and many others that need similarity searching as a necessary supporting service. Traditionally, SISAP conferences have put emphasis on the distance-based searching, but in general the conference concerns both the effectiveness and efficiency aspects of any similarity search approach.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.