Эффективный подход на основе машинного обучения к решению задачи о максимальной клике
In this paper a new approach for solving the maximum clique problem is presented. For a given graph the suggested approach uses machine learning technique to predict the fastest algorithm from several algorithms for the maximum clique problem. Then the chosen algorithm is applied for solving the maximum clique problem in this graph. The computational results show the efficiency of the proposed approach.
In this paper, we summarize the results of recent studies on the application of pattern mining and machine learning to the analysis of demographic sequences. The main goal is the demonstration of demographers’ needs, including next-event prediction and the extraction of interesting patterns from substantial datasets of demographic data, which cannot be handled by conventional demographic techniques. We use decision trees as a technique for demographic event prediction, and emerging sequential patterns and pattern structures for discovering relevant interpretable sequences. The emerging problem statements and positive prospects of the usage of pattern mining in the demography domain are worth dissemination in the data mining community.
A simple measure of similarity for the construction of the market graph is proposed. The measure is based on the probability of the coincidence of the signs of the stock returns. This measure is robust, has a simple interpretation, is easy to calculate and can be used as measure of similarity between any number of random variables. For the case of pairwise similarity the connection of this measure with the sign correlation of Fechner is noted. The properties of the proposed measure of pairwise similarity in comparison with the classic Pearson correlation are studied. The simple measure of pairwise similarity is applied (in parallel with the classic correlation) for the study of Russian and Swedish market graphs. The new measure of similarity for more than two random variables is introduced and applied to the additional deeper analysis of Russian and Swedish markets. Some interesting phenomena for the cliques and independent sets of the obtained market graphs are observed.
In this chapter, we present our enhancements of one of the most efficient exact algorithms for the maximum clique problem—MCS algorithm by Tomita, Sutani, Higashi, Takahashi and Wakatsuki (in Proceedings of WALCOM’10, 2010, pp. 191–203). Our enhancements include: applying ILS heuristic by Andrade, Resende and Werneck (in Heuristics 18:525–547, 2012) to find a high-quality initial solution, fast detection of clique vertices in a set of candidates, better initial coloring, and avoiding dynamic memory allocation. A good initial solution considerably reduces the search tree size due to early pruning of branches related to small cliques. Fast detecting of clique vertices is based on coloring. Whenever a set of candidates contains a vertex adjacent to all candidates, we detect it immediately by its color and add it to the current clique avoiding unnecessary branching. Though dynamic memory allocation allows to minimize memory consumption of the program, it increases the total running time. Our computational experiments show that for dense graphs with a moderate number of vertices (like the majority of DIMACS graphs) it is more efficient to store vertices of a set of candidates and their colors on stack rather than in dynamic memory on all levels of recursion. Our algorithm solves p_hat1000-3 benchmark instance which cannot be solved by the original MCS algorithm. We got speedups of 7, 3000, and 13000 times for gen400_p0.9_55, gen400_p0.9_65, and gen400_p0.9_75 instances, correspondingly.
Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute an upper bound on the clique number for every subproblem. This technique reasonably promises tight bounds on average, but never tighter than the chromatic number of the graph.
Li and Quan, 2010, AAAI Conference, p. 128–133 describe a way to compute even tighter bounds by reducing each colored subproblem to maximum satisfiability problem (MaxSAT). Moreover they show empirically that the new bounds obtained may be lower than the chromatic number.
Based on this idea this paper shows an efficient way to compute related “infra-chromatic” upper bounds without an explicit MaxSAT encoding. The reported results show some of the best times for a stand-alone computer over a number of instances from standard benchmarks.
This book constitutes the post-conference proceedings of the 4th International Conference on Machine Learning, Optimization, and Data Science, LOD 2018, held in Volterra, Italy, in September 2018.The 46 full papers presented were carefully reviewed and selected from 126 submissions. The papers cover topics in the field of machine learning, artificial intelligence, reinforcement learning, computational optimization and data science presenting a substantial array of ideas, technologies, algorithms, methods and applications.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.