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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.


A polynomial algorithm for one problem of guillotine cutting  By: Arslanov, M. OPERATIONS RESEARCH LETTERS  Volume: 35   Issue: 5   Pages: 636-644 Published: SEP 2007

Polynomial algorithms for guillotine cutting of a rectangle into small rectangles of two kinds By: Arslanov, M.; Ashigaliev, D.; Ismail, E. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH  Volume: 185   Issue: 1   Pages: 105-121   Published: FEB 16 2008

Arslanov M.Z. An algorithm of optimum cutting a rectangle into rectangles with two heights / American Journal of Operations Research. – 2014. – №1. – p.12-14.

Arslanov M.Z. A polynomial algorithm of optimum cutting a rectangle into rectangles with two heights // Problems of computer science, 2014, No 4, p. 3-28.

L.Nayzabaeva, S.A.Musstafin. About possibilities of manipulating virtual 3D objects with the help of real objects. Problems of computer science, SB RAS. - 2014, No. 4

Mustafin S. «About the determination of optimal trajectory condition of stowage material», International Conference “Computational and Informational Technologies in Science, Engineering and Education” (CITech-2015), Almaty, Kazakhstan, 2015

E. Amirgaliyev, T.Lovazov, S. Musstafin  About development of the application for mobile robot control, Bulletin of the SDU-2015, No. 1, 146-148