Hamiltonian path rapid solving method based on triangular expansion

Abstract

The invention relates to the field of computer graphics and geographic information science, and particularly discloses a Hamiltonian path rapid solving method based on triangular expansion, which comprises the following steps: S1, acquiring node sample data; s2, constructing a Thiessen polygon network; s3, searching any two adjacent Thiessen polygons, and connecting nodes in the two Thiessen polygons by using a connecting line; s4, searching any Thiessen polygon which is adjacent to the two reference polygons at the same time; s5, connecting the two nodes of the initial connecting line with the nodes in the searched Thiessen polygon to obtain a triangle; s6, deleting the initial connecting lines of the triangle, taking the remaining two connecting lines as the initial connecting lines, andreturning to the step S4; and S7, repeating the step S4S6 until all nodes are searched. The Hamiltonian path rapid solving method based on triangular expansion is simple in principle, can effectivelyreduce the processing difficulty, cost and time, and improves the solving efficiency.

Description

technical field [0001] The invention relates to the fields of computer graphics and geographic information science, in particular to a fast solving method for a Hamiltonian path based on triangular expansion. Background technique [0002] The Hamiltonian problem solving method, that is, the Hamiltonian path problem, is a research hotspot in mathematics and computer graphics, and has great application potential in logistics, resource allocation, military and other fields. The solution method of the Hamiltonian ring problem belongs to the search problem of necessary nodes, and its characteristic is that each node is only connected to two adjacent nodes to form a closed loop. This problem is a connection problem, which belongs to a one-dimensional space problem, and the samples of this problem are expanded in a two-dimensional environment, so the solution of this problem has a difficult dimensional upgrade, but the traditional Hamiltonian path problem method is mostly based on ...

AI Technical Summary

Problems solved by technology

This problem is a connection problem, which belongs to a one-dimensional space problem, and the samples of this problem are expanded in a two-dimensional environment, so the solution of this problem has a difficult dimensional upgrade, but the traditional Hamiltonian path problem method is mostly based on graph theory and From a mathematical point of view, its efficiency and accuracy are not satisfactory, and the spatial position and topological relationship of nodes are ignored

In addition, when the sample data reaches a certain amount when solving the Hamiltonian path problem, computers and traditional algorithms will be powerless

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