This line of research in the Institute of Mathematics was originated in
the early 60’s by prominent scientists in the field of mathematical cybernetics
Academician Yu. I. Zhuravlev and Corresponding Member of the USSR
AS A. A. Lyapunov (1911-1973). Large interest to the problems
of cybernetics, which was shown at that time, and also brilliant scientific
and organizational capabilities of the leaders promoted fast growth of the
collective of cyberneticists and formation of the following main directions:
discrete analysis;
operations research;
methods of combinatorial and discrete optimization;
graph theory;
theory of programming;
mathematical biology;
mathematical linguistics.
Scientific contacts with collectives of cyberneticists from Moscow, Gor’kii,
Kiev, Minsk, Sverdlovsk and other cities were actively maintained. Theoretical
investigations being conducted were closely linked to applied works. Filling
orders for various branches of national industry led to new real-life
problems and a diversification of investigations.
At present, the Department of Theoretical Cybernetics consists of the
following laboratories:
operations research (headed by V. T. Dement’ev);
numerical methods of the theory of optimal processes (headed by V. M. Aleksandrov);
Investigations are carried on in the following main directions:
in the field of discrete analysis: synthesis and complexity of controlling
systems, discrete metric spaces, combinatorics and coding theory, control
and testing of discrete devices;
in the field of operations research: standardization and allocation,
multilevel decision making, net planning and control, routing and packing,
optimal synthesis and functioning of communication nets works, scheduling
theory;
in the field of graph theory: coloring problems, investigation of
planar graphs and various characteristics of graphs;
in the field of methods of optimization and optimal control: design
and analysis exact and approximation algorithms with estimates for solution
of discrete extremal problems, construction of quasioptimal solutions
for problems of optimal control.
Many results were published in volumes of proceedings of the Institute
“Discrete Analysis”, “Upravlyaemye Systemy” and in the journal “Discrete
Analysis and Operations Research”.
Research scientist of the Department carry on teaching work at the Theoretical
Cybernetics, Department of NSU (Novosibirsk State University). Over 500
undergraduates of the Faculty of Mechanics and Mathematics did research
and practical work in the Department. The best of them became research
scientists of the Institute of Mathematics, defended candidate and doctor
theses.
The Department was repeatedly an organizer of all-Union and international
conferences on problems of theoretical cybernetics and operations research.
