The Travelling Salesman Problem ( TSP ) is one of the most difficult problems that many scholars all over the world are studying. This paper points out the disparity between the definition and the classical solution...The Travelling Salesman Problem ( TSP ) is one of the most difficult problems that many scholars all over the world are studying. This paper points out the disparity between the definition and the classical solution to TSP and its practical applications, and then presents a new definition of TSP and its effective algorithm conforming to practical applications, thus making TSP practically more valuable.展开更多
The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations...The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion.It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary:(1)one-class-case algorithm for waves interacting through scales,and(2)two-class-case algorithm for waves interacting through phases.In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-classcase generic algorithm.展开更多
文摘The Travelling Salesman Problem ( TSP ) is one of the most difficult problems that many scholars all over the world are studying. This paper points out the disparity between the definition and the classical solution to TSP and its practical applications, and then presents a new definition of TSP and its effective algorithm conforming to practical applications, thus making TSP practically more valuable.
文摘The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion.It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary:(1)one-class-case algorithm for waves interacting through scales,and(2)two-class-case algorithm for waves interacting through phases.In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-classcase generic algorithm.
