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Periodic Partial Words and Random Bipartite Graphs

Idiatulina L. A., Shur A. M.

Fundamenta Informaticae

2014

Vol. 132, nr 1

15--31

The interaction property (or the Fine-Wilf property) for periodic partial words is studied. Partial words with two periods are represented by bipartite graphs and the interaction property is related to the edge connectedness property of these graphs. Threshold functions for the edge connectedness of random bipartite graphs and multigraphs are found. As a corollary, the interaction property is described in probabilistic terms.

Random graphs for performance evaluation of recommender systems

Chojnacki Sz., Kłopotek M. A.

Control and Cybernetics

2011

Vol. 40, no 2

237-257

The purpose of this article is to introduce a new analytical framework dedicated to measuring performance of recommender systems. A standard approach is to assess the quality of a system by means of accuracy related statistics. However, the specificity of the environments in which recommender systems are deployed requires paying much attention to speed and memory requirements of the algorithms. Unfortunately, it is implausible to assess accurately the complexity of various algorithms with formal tools. This can be attributed to the fact that such analyses are usually based on an assumption of dense representation of underlying data structures. In real life, though, the algorithms operate on sparse data and are implemented with collections dedicated for them. Therefore, we propose to measure the complexity of recommender systems with artificial datasets that posses real-life properties. We utilize a recently developed bipartite graph generator to evaluate how the state-of-art recommender system behavior is determined and diversified by topological properties of the generated datasets.

Stochastic version of the Erdos-Renyi limit theorem

Khorunzhy A.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

221--230

We generalize the Erdös-Rényi limit theorem on the maximum of partial sums of random variables to the case when the number of terms in these sums in randomly distributed. Relations between this limit theorem and the spectral theory of random graphs and random matrices are discussed.

Parsing of random graphs for scene analysis

Skomorowski M.

Machine Graphics and Vision

1998

Vol. 7, No. 1/2

313-323

Further results of research into parsing of random graphs for recognition of distored scenes ([9, 11]) are presented. An efficient top-down parallel parsing algorithm for analysis of distored scenes is proposed. The proposed approach involves parsing of graph grammars. To take into acount all variations of a distored scene under study, a probabilistic description of the scene is needed. The random graph approach ([9, 11]) is proposed here for such a description.