The subject of the paper is to analyze the problem of the frequency of the subsequences in large volume sequences. A new probabilistic algorithm for mining frequent sequences (ProMFS) is proposed. In the abstract of this paper we get know information about the main concepts of the analysis this problem. We got acquainted with the Market Basket Data example which main idea is to find most frequent set of the customer’s selected items. There were also presented several algorithms, which analyze the problems of finding the frequent sequences. The most popular algorithms are: Apriori – based on the property: “Any subset of a large item set must be large”, Eclat – the main feature is dynamically process each transaction online maintaining 2-itemset counts, GSP algorithm – which can be used to identify surely not frequent sets. According to the results of these algorithms the new probabilistic algorithm for mining frequent sequences was implemented. The new algorithm is based on the estimation of the statistical characteristic of the main sequence. According to these characteristics we generated much shorter model sequence that is analyzed with the GSP algorithm. The subsequence frequency in the main sequence is estimated by the results of the GSP algorithm applied on the new sequence. The new probabilistic algorithm implemented in the practical part we tested in some experiments. There were two programs used – the first one was created in Pascal language, the second in Delphi... [to full text]

In general, subset sum problem is strongly believed to be computationally difficult to solve. But in 1983, Lagarias and Odlyzko proposed a probabilistic algorithm for solving subset sum problems of sufficiently low density in polynomial time. In 1991, Coster et. al. improved the Lagarias-Odlyzko algorithm and solved subset sum problems with higher density. Both algorithms reduce subset sum problem to finding shortest non-zero vectors in special lattices. In this thesis, we first proposed a new viewpoint to define the problems which can be solved by this two algorithms and shows the improved algorithm isn't always better than the Lagarias-Odlyzko algorithm. Then we verify this notion by experimentation. Finally, we find that the Lagrias-Odlyzko algorithm can solve the high-density subset sum problems if the weight of solution is higher than 0.7733n or lower than 0.2267n, even the density is close to 1.

This work describes path finding among obstacles in 3D space using probabilistic algorithms. Users can create scene in application GUI - define start object, obstacles, goal position and run probabilistic algorithm. The finding path is visualized. The work describes probabilistic algorithm, collision detection and the basics of 3D graphics and shows design and implementation of an application created.

This work deals with the path finding for nonholonomic robots using probabilistic algorithms. The theoretical part analyzes the general problem of finding routes. Subsequently, the work will focus on probabilistic algorithms. The practical part describes design of the applet and web sites that demonstrate probabilistic algorithms to user-specified objects.