分形网络与复杂空间解集的算法转换模型

空间上看来简单的问题在时间上可能导致非常复杂的计算问题,而时间上的计算问题一旦在空间上采用某种有序划分,复杂过程又可以约化为简单的处理程序.分形思想为这类有序划分提供了可取的思路.借助分形思想和“分而治之“的策略,可望将复杂问题的“穷尽处理法“变为“有限选择法“,从而找到虽非最优但可满意的解决方案.以经典的TSP为例,提出空间系统复杂计算问题的处理方法,这种方法有助于实现指数算法与多项式算法的实用转换过程.

Fractal Networks and Algorithmic Transformation of Complex Spatial Disaggregation

Many seemingly simple problems in space can lead to uncomputability associated with complexity in time,while the uncomputable problems in time can be solved in satisfying way by means of spatial disaggregation.Taking travelling salesman problem(TSP) as an example,this paper illustrates how to change a seemingly unsolvable complex problem into a solvable simple problem in practice.Using the ideas from fractals and strategy of 'dividing-and-ruling' geographical space,the spatial search problems(SSP) for optimum solutions through brute force methods can be converted into problems of selection in limited projects.A model is made in order to change the exponential algorithm into polynomial algorithm.By way of the model of algorithm transformation,the uncomputable problem becomes computable.Even though the results are not optimum,they are considerable good ones.