Variable Formulation and Neighborhood Search Methods for the Maximum Clique Problem in Graph

Doktorska disertacija se bavi temama rešavanja računarski teških problema kombinatorne optimizacije. Istaknut je problem maksimalne klike kao predstavnik određenih struktura u grafovima. Problem maksimalne klike i sa njim povezani problemi su formulisani kao nelinearne funkcije. Rešavani su sa ciljem otkrivanja novih metoda koje pronalaze dobre aproksimacije rešenja za neko razumno vreme. Predložene su varijante Metode promenljivih okolina na rešavanje maksimalne klike u grafu. Povezani problemi na grafovima se mogu primeniti na pretragu informacija, raspoređivanje, procesiranje signala, teoriju klasifikacije, teoriju kodiranja, itd. Svi algoritmi su implementirani i uspešno testirani na brojnim različitim primerima.This Ph.D. thesis addresses topics NP hard problem solving approaches in combinatorial optimization and according to that it is highlighted maximum clique problem as a representative of certain structures in graphs. Maximum clique problem and related problems with this have been formulated as non linear functions which have been solved to research for new methods and good solution approximations for some reasonable time. It has been proposed several different extensions of Variable Neighborhood Search method. Related problems on graphs could be applied on information retrieval, scheduling, signal processing, theory of classi_cation, theory of coding, etc. Algorithms are implemented and successfully tested on various different tasks