Laboratory of pattern recognition and decision-making named after prof. Aidarkhanov M.B.

Head of the laboratory Dr.Sc. (Phys.-Math.),

Prof. M.Z. Arslanov

Development and study of mathematical models and methods for decision-making problems. Recognition and classification, analysis, processing and transmission of data. Efficient algorithms of combinatorial optimization.

Efficient polynomial algorithms for problems of rectangular cutting have been designed.

An efficient polynomial algorithm of optimal packaging of unit squares in the hypograph of piecewise linear function has been developed for the problem 56 from the list of unsolved problems «The Open Problems Project».

Theorems on properties of a group synthesis have been proved, models, methods and algorithms of group synthesis have been designed and studied to solve problems of classification and pattern recognition.

Mathematical models and problems equivalency methods have been presented in the problem of rectangular cutting, and parameters decrease algorithms in rectangular cutting.

  • The duality theorem in rectangular cutting has been proved.
  • Methods, models and polynomial algorithms of building the convex cover of problem solutions of cutting a cuboid into two smaller cuboids have been developed and studied.

Obtained intellectual property certificates and Patents

  1. Authorship certificate 009126. Program for partitioning multidimensional vectors into classes / S.A.Musstafin, M.Z.Arslanov, S.M. Grechko; publ. 2017. – p 25.
  2. Authorship certificate 007940. Program for partitioning a rectangular sheet into smaller rectangles / S.A.Musstafin, M.Z.Arslanov, S.M. Grechko; publ. 2017. – p 20.