Advanced Combinatorial Optimization - Aslanyan, L. (Mathematical Problems of Computer Science, 2021)
The research aims at constructing efficient algorithms and approximations for hard, open and novel combinatorial optimization problems with emphasis on the practical applicability of results. Boolean minimization (hard), Isoperimetry and tomography (open), decentralized and stream analysis (novel) algorithms are considered. Combinatorial reduction is another target, being related with two sets of problem instances, together with a structure of reduction. This triplet is studied to recover the tractability and approximation boundaries. The concept of optimality that is not yet clear for complex systems with conflicting goals is addressed in terms of heuristics, stability and equilibria. These issues play a key-role to the emergence of a major research pole in the area of combinatorial optimization, highly responsive to the industry needs and tightly linked to different research are as with design, analysis and management of complex systems. Applied areas addressed include Population Genomics and Wireless Sensor Networks.