Прикладные аспекты использования алгоритмов ранжирования для ориентированных взвешенных графов(на примере графов социальных сетей)

The article deals with the applied aspects of the preliminary vertices ranking for oriented weighted graph. In this paper, the authors observed the widespread use of this technique in developing heuristic discrete optimization algorithms. The ranking problem is directly related to the problem of social networks centrality and large real world data sets but as shown in the article ranking is explicitly or implicitly used in the development of algorithms as the initial stage of obtaining a solution for solving applied problems. Examples of such ranking application are given. The examples demonstrate the increase of efficiency for solving some optimization applied problems, which are widely used in mathematical methods of optimization, decision-making not only from the theoretical development point of view but also their applications. The article describes the structure of the first phase of the computational experiment, which is associated with the procedure of obtaining test data sets. The obtained data are presented by weighted graphs that correspond to several groups of the social network Vkontakte with the number of participants in the range from 9000 to 24 thousand. It is shown that the structural characteristics of the obtained graphs differ significantly in the number of connectivity components. Characteristics of centrality (degree's sequences), as shown, have exponential distribution. The main attention is given to the analysis of three approaches to graph vertices ranking. We propose analysis and comparison of the obtained set of ranks by the nature of their distribution. The definition of convergence for graph vertex ranking algorithms is introduced and the differences of their use in considering the data of large dimension and the need to build a solution in the presence of local changes are discussed.Рассматриваются прикладные аспекты использования предварительного ранжирования вершин ориентированного взвешенного графа. Особое внимание уделяется широкому использованию такого приема в разработке эвристических алгоритмов дискретной оптимизации. Задача ранжирования имеет непосредственное отношение к проблеме определения центральности в социальных сетях, обработке больших массивов данных реального мира, но как показано в статье, явно или косвенно используется при разработке алгоритмов решения прикладных задач в качестве начального этапа построения решения. Приводятся примеры использования предварительного ранжирования, в которых продемонстрировано повышение эффективности решения некоторых прикладных задач, имеющих широкое применение в математических методах оптимизации. Дано описание структуры первой фазы вычислительного эксперимента, которая связана с получением тестовых наборов данных. Полученные данные представлены взвешенными графами, которые соответствуют нескольким группам социальной сети ВКонтакте с числом вершин в диапазоне от 9000 до 24 тысяч участников. Показано, что структурные характеристики полученных графов по числу компонент связности существенно различаются. Продемонстрированы некоторые характеристики центральности (распределения степенных последовательностей), которые имеют экспоненциальный характер. Основное внимание уделяется анализу трех алгоритмов построения иерархии ранжирования вершин графов, предлагаются новые подходы к вычислению рангов вершин с использованием информации об активности пользователей в социальных сетях. Проводится сравнение распределений полученных совокупностей рангов. Вводится понятие сходимости алгоритмов ранжирования вершин графов, а также обсуждаются различия их использования при рассмотрении данных большой размерности и необходимости построения решения в случае учета только локальных изменений

Lazy Decomposition for Distributed Decision Procedures

The increasing popularity of automated tools for software and hardware verification puts ever increasing demands on the underlying decision procedures. This paper presents a framework for distributed decision procedures (for first-order problems) based on Craig interpolation. Formulas are distributed in a lazy fashion, i.e., without the use of costly decomposition algorithms. Potential models which are shown to be incorrect are reconciled through the use of Craig interpolants. Experimental results on challenging propositional satisfiability problems indicate that our method is able to outperform traditional solving techniques even without the use of additional resources.Comment: In Proceedings PDMC 2011, arXiv:1111.006

Fast Statistical Alignment

We describe a new program for the alignment of multiple biological sequences that is both statistically motivated and fast enough for problem sizes that arise in practice. Our Fast Statistical Alignment program is based on pair hidden Markov models which approximate an insertion/deletion process on a tree and uses a sequence annealing algorithm to combine the posterior probabilities estimated from these models into a multiple alignment. FSA uses its explicit statistical model to produce multiple alignments which are accompanied by estimates of the alignment accuracy and uncertainty for every column and character of the alignment—previously available only with alignment programs which use computationally-expensive Markov Chain Monte Carlo approaches—yet can align thousands of long sequences. Moreover, FSA utilizes an unsupervised query-specific learning procedure for parameter estimation which leads to improved accuracy on benchmark reference alignments in comparison to existing programs. The centroid alignment approach taken by FSA, in combination with its learning procedure, drastically reduces the amount of false-positive alignment on biological data in comparison to that given by other methods. The FSA program and a companion visualization tool for exploring uncertainty in alignments can be used via a web interface at http://orangutan.math.berkeley.edu/fsa/, and the source code is available at http://fsa.sourceforge.net/

Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Our second algorithm handles an arbitrary sequence of arc additions in $O(n^{5/2})$ time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take $\Omega(n^2 2^{\sqrt{2\lg n}})$ time by relating its performance to a generalization of the $k$-levels problem of combinatorial geometry. A completely different algorithm running in $\Theta(n^2 \log n)$ time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.Comment: 31 page

ECROs: Building global scale systems from sequential code

Funding Information: We would like to thank Matteo Marra, Jim Bauwens, and the anonymous reviewers for their comments which helped improve the paper. Kevin De Porre is funded by an SB Fellowship of the Research Foundation - Flanders. Project number: 1S98519N. This work was partially supported by Fundação para a Ciência e a Tecnologia - Portugal (FCT/MCTES) under grants UIDB/04516/2020, PTDC/CCI-INF/32081/2017, and LISBOA-01-0145-FEDER-032662/PTDC/CCI-INF/32662/2017.To ease the development of geo-distributed applications, replicated data types (RDTs) offer a familiar programming interface while ensuring state convergence, low latency, and high availability. However, RDTs are still designed exclusively by experts using ad-hoc solutions that are error-prone and result in brittle systems. Recent works statically detect conflicting operations on existing data types and coordinate those at runtime to guarantee convergence and preserve application invariants. However, these approaches are too conservative, imposing coordination on a large number of operations. In this work, we propose a principled approach to design and implement efficient RDTs taking into account application invariants. Developers extend sequential data types with a distributed specification, which together form an RDT. We statically analyze the specification to detect conflicts and unravel their cause. This information is then used at runtime to serialize concurrent operations safely and efficiently. Our approach derives a correct RDT from any sequential data type without changes to the data type's implementation and with minimal coordination. We implement our approach in Scala and develop an extensive portfolio of RDTs. The evaluation shows that our approach provides performance similar to conflict-free replicated data types for commutative operations, and considerably improves the performance of non-commutative operations, compared to existing solutions.publishersversionpublishe