Research On Matrix Algorithm Of Simple Graph Problem

With the development of science and technology and the progress of the times,the basic problem in many real-life applications,such as travel routes,car navigation,logistics planning,city planning route calculation is needed as soon as possible out of the most reasonable path.Many experts and scholars in the unremitting efforts,although progress has been made many breakthrough,but now the face of common engineering application of large-scale data and complex needs,the algorithm still has many imperfections.On the basis of referring to the existing algorithms,this thesis introduces the connection matrix multiplication algorithm to find the shortest or longest path for the path problem of simple graphs.Because a simple graph can correspond to an adjacency matrix,we can use matrix method to find the shortest path and the longest path problem of simple graphs.By introducing the concept of adjacency matrix and define the path diagram multiplication,can detect the corresponding weight,also can find the optimal distance between any two points and the corresponding all paths,can also find all paths with length constraints,and easier to program operation.In this thesis a simple graph path problem,gives the concept of two-dimensional matrix elements,the weighted graph corresponding weight matrix defines the initial two-dimensional weighted path matrix and general two-dimensional weighted path matrix,the weighting matrix multiplication operation is defined based on the path of "multiplication" operation,which obtained a general weighted path matrix multiplication "operation,and then through the" multiplication "operation to find all the points on the shortest path and the longest path and the shortest distance corresponding to the longest distance,the results displayed in the final general weighted path matrix.The design idea of this algorithm is simple and the calculation method is not complicated.It depends on the high-speed computing of the computer,and it is more efficient for the solution of large-scale simple graphs.At the same time,it has important practical significance and reference value for the realization of other algorithm’s program code and the promotion of performance.It provides an efficient solution for the practical application of simple graph path problem.