Algebrization and randomization methods

Abstract

Over the past decades, people have dedicated great efforts to solve some NP- complete problems. Hamiltonian path problem is one of classic problems which baffle people many years. In recent years, some algebrization and randomization techniques have been developed and applied in the design of algorithms, which provides a credible alternative to traditional methods. Then the testing monomials theories were developed based on above techniques, which have been found applications in solving some critical problems in graph theory, networking, bioinformatics, etc. We give a self-contained description of the examples of successful applications by combining algebrization techniques and randomization techniques.