Input Vertices Research Articles

Finding Minimum Connected Subgraphs With Ontology Exploration on Large RDF Data

In this paper, we study the following problem: given a knowledge graph (KG) and a set of input vertices (representing concepts or entities) and edge labels, we aim to find the smallest connected subgraphs containing all of the inputs. This problem plays a key role in KG-based search engines and natural language question answering systems, and it is a natural extension of the Steiner tree problem, which is known to be NP-hard. We present RECON, a system for finding approximate answers. RECON aims at achieving high accuracy with instantaneous response (i.e., sub-second/millisecond delay) over KGs with hundreds of millions edges without resorting to expensive computational resources. Furthermore, when no answer exists due to disconnection between concepts and entities, RECON refines the input to a semantically similar one based on the ontology, and attempts to find answers with respect to the refined input. We conduct a comprehensive experimental evaluation of RECON. In particular we compare it with five existing approaches for finding approximate Steiner trees. Our experiments on four large real and synthetic KGs show that RECON significantly outperforms its competitors and incurs a much smaller memory footprint.

Algorithm for finding subcritical paths on network diagrams

Objectives . Network diagrams are used as an information support element in planning and project management processes for structuring planned work and calculating project efficiency characteristics. In order to optimize and balance resources used in projects, it becomes necessary to locate in these models not only the critical path of the maximum weighted length, but also the subcritical paths closest to it having a shorter length in relation to it. The aim of the work is to synthesize and analyze an algorithm for finding k -shortest paths between the input and output network vertices, on which basis the above-mentioned subcritical paths can be identified. Methods . The provisions of graph theory and group theory, as well as the method of dynamic programming, were used. Results . An algorithm for finding k- shortest paths in contourless directed graphs having a strict order relation was developed. Abstract elements were defined according to group theory in graphs as p- contours, between which a multilevel structure of relations for implementing the necessary search of paths was then established. For substantiating the efficiency of the constructed algorithm, the validity of the main provisions was demonstrated as follows: firstly, the multilevel system of relations is exhaustive; secondly, there is no loss in the final solution during the operation of the algorithm; thirdly, the paths obtained as a result of the work of the algorithm satisfy the main required relation between them. Numerically, the algorithm was implemented by the dynamic programming method extended by means of an additional functional relationship, implying the presence of suboptimal policies. Conclusions . The conducted runs of computational experiments confirmed the operability and efficiency of the software-implemented algorithm. The performed analysis demonstrated the good convergence characteristics of the proposed algorithm as compared with other algorithms of this class applied to network diagrams. On this basis, it can be recommended for practical use in project management information systems.

Business processes monitoring based on fuzzy cognitive maps

The subject matter of the article is a toolkit and monitoring processes of weakly structured business processes using fuzzy cognitive maps (FCMs). The goal is to create a model for monitoring and forecasting the course of business processes based on the FCMs, which provide flexibility and the ability to adapt to the conditions of changing circumstances in the process to be monitored, as well as insurance of the possibility of applying unstable FCM.s The task is to develop a formal monitoring system model; develop a computational FCM model; develop a method of using unstable FCMs: to develop a method for creating and using an FCM model. The methods used are graph modeling methods and computational experiment methods. The following results were obtained. A formal model of the system of monitoring and coordination of decisions regarding the course of business processes has been developed. A model of a weighted semantic graph was developed, which includes three types of vertices, namely, input vertices that will receive subjective evaluations of users regarding the course of the process, intermediate vertices that correspond to factors important from the perspective of the decision-maker, and final vertices that reflect integral evaluations of the quality of business process execution. A computational FCM model has been developed, which can adapt to the specifics of business logic due to the flexible adjustment of memory parameters and connections between FCM nodes. A method of using unstable FCMs has been developed. A methodology for creating and using FCMs designed for monitoring weakly structured business processes has been developed. Conclusions. The scientific novelty of the work is as follows: the model for monitoring and forecasting the course of business processes due to the use of a fuzzy cognitive map, in which the parameters of the importance and node memory and connections provide additional flexibility and the possibility of coordination and adaptation in the conditions of changing circumstances in the process to be monitored has been improved; a method of using unstable FCMs by setting limits on the values of the nodes excitation and using as a measure of excitation not only stable excitation values of FCM nodes but also the rate of growth of excitation values as an indicator of trends, which allows monitoring and forecasting the course of business processes has been proposed.

Geometric graph-theoretic aspects of quantum stabilizer codes

We propose a systematic procedure for the construction of graphs associated with binary quantum stabilizer codes. The procedure is characterized by means of the following three step process. First, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code. Second, the canonical form of the CWS code is determined and third, the input vertices are attached to the graphs. In order to verify the effectiveness of the procedure, we implement the Gottesman stabilizer code characterized by multi-qubit encoding operators for the resource-efficient error correction of arbitrary single-qubit errors. Finally, the error-correcting capabilities of the Gottesman eight-qubit quantum stabilizer code is verified in graph-theoretic terms as originally advocated by Schlingemann and Werner.

УПРАВЛІННЯ ЗБУТОМ ПІДПРИЄМСТВА НА ОСНОВІ ВИКОРИСТАННЯ ДІАГРАМИ ІСІКАВИ

Marketing research at an enterprise is carried out by marketing units in order to determine a possible increase in the marketing activity of the enterprise. To identify the strengths and weaknesses of the sales management of the enterprise, the SWOT-analysis method was applied. A matrix of SWOT analysis of company's sales activity was built, which forms squares in the form of a combination of the following factors: "Strengths-Opportunities" (SO), "Strengths-Threats" (ST), "Weaknesses-Possibilities" (WO), "Weaknesses-Threats" (WT). The most significant intersections of the SWOT matrix factors of the analysis were analyzed, and it was proposed to use four types of strategies on their basis. To formalize cause-and-effect relations Ishikawa diagram was used. In the constructed diagram, the sales activity of the enterprise depends on 5 main groups of characteristics. It is suggested the management of sales activities of the enterprise based on the expansion of the target market, which is characterized by factors (linguistic variables) competitive environment (T1), market segmentation (T2), quality of advertising (T3), digital marketing (T4), product quality (T5) and sales activity (T6). Due to the great uncertainty of the factors influencing sales activities, a solution to the problem of sales management is proposed, which is based on the representation of the system in the form of a fuzzy cognitive map. Establishing links between input (T1,…, T5) and output (T6) vertices allows you to build a fuzzy cognitive map of the sales management process of the enterprise, in the form of an oriented graph based on the adjacency matrix. In the constructed model of the oriented graph all actions of factors (vertices) on each other are in an interval [0; 1]. Therefore, this model is presented as a structural model of the sales management process of the enterprise. It is concluded that a more accurate model can be constructed by giving the arcs of the oriented graph numerical values (weights). The weight of the arcs is interpreted as the force of influence of the factor, and the sign can be both positive (increase in influence) and negative (decrease in influence).

Fast and robust mesh arrangements using floating-point arithmetic

We introduce a novel algorithm to transform any generic set of triangles in 3D space into a well-formed simplicial complex. Intersecting elements in the input are correctly identified, subdivided, and connected to arrange a valid configuration, leading to a topologically sound partition of the space into piece-wise linear cells. Our approach does not require the exact coordinates of intersection points to calculate the resulting complex. We represent any intersection point as an unevaluated combination of input vertices. We then extend the recently introduced concept of indirect predicates [Attene 2020] to define all the necessary geometric tests that, by construction, are both exact and efficient since they fully exploit the floating-point hardware. This design makes our method robust and guaranteed correct, while being virtually as fast as non-robust floating-point based implementations. Compared with existing robust methods, our algorithm offers a number of advantages: it is much faster, has a better memory layout, scales well on extremely challenging models, and allows fully exploiting modern multi-core hardware with a parallel implementation. We thoroughly tested our method on thousands of meshes, concluding that it consistently outperforms prior art. We also demonstrate its usefulness in various applications, such as computing efficient mesh booleans, Minkowski sums, and volume meshes.

On Mathematical Aspects of Analyzing the Structure of Complex Systems Using Weighted Digraphs

The paper deals with the structure of complex systems represented as directed graphs with the values assigned to a graph’s vertices and edges. The natural procedure of determining the values of vertices through the input ones is introduced. The formulas are proved in order to calculate the influence of input vertices to others in case of linear relations. These formulas are closely connected with the internal structure of considered graph. The example of application of the formulas is described.

ОЦЕНКА РЕЗУЛЬТАТИВНОСТИ ПРОЦЕССА ПРОЕКТИРОВАНИЯ АВИАДВИГАТЕЛЕЙ С ПОМОЩЬЮ ГРАФОВ

The role of the aircraft engine design process effectiveness evaluating as an integral part of monitoring, measuring, and analyzing this process in the overall enterprise quality management system is considered. The general approach to the effectiveness evaluation and analysis is analyzed. It is noted that in the effectiveness evaluation, both integral indicators and calculations made for all the constituent elements of the process indicators should be determined. In order to identify the root causes of obtaining unsatisfactory performance indicators, each criterion is examined in detail, analyzing the results of each individual unit participation in the design process. For the analysis of quantitative indicators of the design process effectiveness, it is proposed to apply processes modeling and analysis using directed (oriented) and non-directional graphs. To carry out a structural analysis of the results, it is proposed to represent the graph in the form of a vertex adjacency matrix. Examples of the design processes effectiveness evaluating are considered according to the indicator “Number of design documents developed in a monitoring time (month)” and according to the indicator “Fulfillment of thematic plans items put under control, the deadlines for which have been postponed”. In the first example, in a directed graph, the group of output vertices consists of the design subdivisions involved in the design, and the group of input vertices consists of the projects that are being designed. The edges of the graph are the quantities of documentation developed by each unit for each project. In the second example, the connection of the output vertices of the graph, which are the design units, with the input vertex is carried out through the edges, on which the number of thematic plan points is set, the deadlines for which were postponed. The process of data mathematical processing recorded in vertex adjacency matrices is described. The proposed methodology application allows the analysis of the enterprise production activity results for each individual indicator of the analyzed process.

A Flow-Network-Based Polynomial-Time Approximation Algorithm for the Minimum Constrained Input Structural Controllability Problem

This paper deals with minimum cost constrained input selection (minCCIS) for state-space structured systems. Our goal is to optimally select an input set from the given inputs such that the system is structurally controllable when the set of states that each input can influence is prespecified and each input has a cost associated with it. This problem is known to be NP-hard. First, we give a flow-network-based novel necessary and sufficient graph theoretic condition for checking structural controllability. Using this condition, we propose a polynomial time reduction of the problem to a known NP-hard problem: the minimum-cost fixed-flow problem (MCFF). Subsequently, we show that approximation schemes of MCFF directly apply to the minCCIS problem. Using the special structure of the flow-network constructed for the structured system, we formulate a polynomial time approximation algorithm based on minimum weight bipartite matching problem and a greedy scheme for solving the MCFF problem on the system flow-network. The proposed algorithm gives a so-called $\Delta$ -approximate solution to MCFF, where $\Delta$ denotes the maximum in-degree of input vertices in the flow-network of the structured system.

Multisided generalisations of Gregory patches

We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided Bézier patches. Our first construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G1 continuity between adjoining Bézier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised Bézier patch structure to allow for cross-boundary derivatives to be defined independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation.

Improved quantum backtracking algorithms using effective resistance estimates

We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain cases exponentially outperform classical procedures (such as DPLL). Some of the previous work focused on obtaining a quantum advantage for trees in which a unique marked vertex is promised to exist. We remove this restriction and re-characterise the problem in terms of the effective resistance of the search space. To this end, we present a generalisation of one of Montanaro's algorithms to trees containing $k \geq 1$ marked vertices, where $k$ is not necessarily known \textit{a priori}. Our approach involves using amplitude estimation to determine a near-optimal weighting of a diffusion operator, which can then be applied to prepare a superposition state that has support only on marked vertices and ancestors thereof. By repeatedly sampling this state and updating the input vertex, a marked vertex is reached in a logarithmic number of steps. The algorithm thereby achieves the conjectured bound of $\widetilde{\mathcal{O}}(\sqrt{TR_{\mathrm{max}}})$ for finding a single marked vertex and $\widetilde{\mathcal{O}}\left(k\sqrt{T R_{\mathrm{max}}}\right)$ for finding all $k$ marked vertices, where $T$ is an upper bound on the tree size and $R_{\mathrm{max}}$ is the maximum effective resistance encountered by the algorithm. This constitutes a speedup over Montanaro's original procedure in both the case of finding one and finding multiple marked vertices in an arbitrary tree. If there are no marked vertices, the effective resistance becomes infinite, and we recover the scaling of Montanaro's existence algorithm.

Array-based Compact Data Structures for Triangulations: Practical Solutions with Theoretical Guarantees

We consider the problem of designing space efficient solutions for representing triangle meshes. Our main result is a new explicit data structure for compactly representing planar triangulations: if one is allowed to permute input vertices, then a triangulation with n vertices requires at most 4n references (5n references if vertex permutations are not allowed). Our solution combines existing techniques from mesh encoding with a novel use of maximal Schnyder woods. Our approach extends to higher genus triangulations and could be applied to other families of meshes (such as quadrangular or polygonal meshes). As far as we know, our solution provides the most parsimonious data structures for triangulations, allowing constant time navigation. Our data structures require linear construction time, and are fast decodable from a standard compressed format without using additional memory allocation. All bounds, concerning storage requirements and navigation performances, hold in the worst case. We have implemented and tested our results, and experiments confirm the practical interest of compact data structures.

Batch Coloring of Graphs

We study two versions of graph coloring, where the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic vertex coloring, the goal is to minimize the maximum color used, and for the sum coloring problem, the goal is to minimize the sum of colors assigned to all input vertices. In the offline variant, the entire graph is presented at once, and in online problems, one vertex is presented for coloring at each time, and the only information is the identity of its neighbors among previously known vertices. In batched graph coloring, vertices are presented in k batches, for a fixed integer $$k \ge 2$$ , such that the vertices of a batch are presented as a set, and must be colored before the vertices of the next batch are presented. This last model is an intermediate model, which bridges between the two extreme scenarios of the online and offline models. We provide several results, including a general result for sum coloring and results for the classic graph coloring problem on restricted graph classes: We show tight bounds for any graph class containing trees as a subclass (forests, bipartite graphs, planar graphs, and perfect graphs, for example), and an interesting result for interval graphs and $$k=2$$ , where the value of the (strict and asymptotic) competitive ratio depends on whether the graph is presented with its interval representation or not.

Size-Treewidth Tradeoffs for Circuits Computing the Element Distinctness Function

In this work we study the relationship between size and treewidth of circuits computing variants of the element distinctness function. First, we show that for each n, any circuit of treewidth t computing the element distinctness function δ n : {0, 1} n → {0, 1} must have size at least $\Omega (\frac {n^{2}}{2^{O(t)} \log n})$ . This result provides a non-trivial generalization of a super-linear lower bound for the size of Boolean formulas (treewidth 1) due to Neciporuk. Subsequently, we turn our attention to read-once circuits, which are circuits where each variable labels at most one input vertex. For each n, we show that any read-once circuit of treewidth t and size s computing a variant τ n : {0, 1} n → {0, 1} of the element distinctness function must satisfy the inequality $t\cdot \log s \geq \Omega (\frac {n}{\log n})$ . Using this inequality in conjunction with known results in structural graph theory, we show that for each fixed graph H, read-once circuits computing τ n which exclude H as a minor must have size at least Ω(n 2/log4 n). For certain well studied functions, such as the triangle-freeness function, this last lower bound can be improved to Ω(n 2/log 2n).

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

Robust free space construction for a polyhedron with planar motion

We present a free space construction algorithm for a polyhedron that translates in thexy plane and rotates around itsz axis, relative to a stationary polyhedron. We employ the proven paradigm of constructing the configuration space subdivision defined by patches that comprise the configurations where the boundary features of the polyhedra are in contact. We implement the algorithm robustly and efficiently. The challenge is to detect degenerate predicates efficiently and to handle them correctly. We use our ACP (Adaptive Controlled Perturbation) robustness strategy to prevent degenerate predicates due to input in special position. The remaining cases are predicates that are identical to the zero polynomial because their arguments are derived from overlapping sets of input vertices. We detect and handle these cases with custom logic. We validate the implementation by computing maximum clearance paths.

DOCUMENT IMAGE REGISTRATION FOR IMPOSED LAYER EXTRACTION

Extraction of filled-in information from document images in the presence of template poses challenges due to geometrical distortion. Filled-in document image consists of null background, general information foreground and vital information imposed layer. Template document image consists of null background and general information foreground layer. In this paper a novel document image registration technique has been proposed to extract imposed layer from input document image. A convex polygon is constructed around the content of the input and the template image using convex hull. The vertices of the convex polygons of input and template are paired based on minimum Euclidean distance. Each vertex of the input convex polygon is subjected to transformation for the permutable combinations of rotation and scaling. Translation is handled by tight crop. For every transformation of the input vertices, Minimum Hausdorff distance (MHD) is computed. Minimum Hausdorff distance identifies the rotation and scaling values by which the input image should be transformed to align it to the template. Since transformation is an estimation process, the components in the input image do not overlay exactly on the components in the template, therefore connected component technique is applied to extract contour boxes at word level to identify partially overlapping components. Geometrical features such as density, area and degree of overlapping are extracted and compared between partially overlapping components to identify and eliminate components common to input image and template image. The residue constitutes imposed layer. Experimental results indicate the efficacy of the proposed model with computational complexity. Experiment has been conducted on variety of filled-in forms, applications and bank cheques. Data sets have been generated as test sets for comparative analysis.

Задача оптимизации вычислений в сетевых структурах

A computer network consisting of n vertices (vertices, which solved some problems), m input vertices and m output vertices ( m is the number of tasks) is considered. Each task matches to way in the network with input H and output K , corresponding to some algorithm of problem solving. At the same time only one task can be solved in each vertex. Therefore, it may be a conflict in the moment of arrival to the vertex of a task if this vertex is busy with another task. The vertices in which several tasks may be solved at the same time, will be called problem vertices. The problems of tasks scheduling according to criteria of minimizing the time required to solve all the problems or minimize the maximum deviation from the required solution time are examined. Methods of local optimization, branch, branch and bound are proposed for their solution.

Exploring Curved Schematization of Territorial Outlines.

Hand-drawn schematized maps traditionally make extensive use of curves. However, there are few automated approaches for curved schematization; most previous work focuses on straight lines. We present a new algorithm for area-preserving curved schematization of territorial outlines. Our algorithm converts a simple polygon into a schematic crossing-free representation using circular arcs. We use two basic operations to iteratively replace consecutive arcs until the desired complexity is reached. Our results are not restricted to arcs ending at input vertices. The method can be steered towards different degrees of "curviness": we can encourage or discourage the use of arcs with a large central angle via a single parameter. Our method creates visually pleasing results even for very low output complexities. To evaluate the effectiveness of our design choices, we present a geometric evaluation of the resulting schematizations. Besides the geometric qualities of our algorithm, we also investigate the potential of curved schematization as a concept. We conducted an online user study investigating the effectiveness of curved schematizations compared to straight-line schematizations. While the visual complexity of curved shapes was judged higher than that of straight-line shapes, users generally preferred curved schematizations. We observed that curves significantly improved the ability of users to match schematized shapes of moderate complexity to their unschematized equivalents.

Bonding vertex sets over distributed graph

Given two sets of vertices in a graph, it is often of a great interest to find out how these vertices are connected, especially to identify the vertices of high prominence defined on the topological structure. In this work, we formally define a V ertex S et B onding query (shorted as VSB), which returns a minimum set of vertices with the maximum importance w.r.t total betweenness and shortest path reachability in connecting two sets of input vertices. We find that such a kind of query is representative and could be widely applied in many real world scenarios, e.g., logistic planning, social community bonding and etc. Challenges are that many of such applications are constructed on graphs that are too large to fit in single server, and the VSB query evaluation turns to be NP-hard. To cope with the scalability issue and return the near optimal result in almost real time, we propose a generic solution framework on a shared nothing distributed environment. With the development of two novel techniques, guided graph exploration and betweenness ranking on exploration, we are able to efficiently evaluate queries for error bounded results with bounded space cost. We demonstrate the effectiveness of our solution with extensive experiments over both real and synthetic large graphs on the Google's Cloud platform. Comparing to the exploration only baseline method, our method achieves several times of speedup.