Approximate solving method for maximum independent set on unit disk graph

Abstract

The invention discloses an approximate solving method for a maximum independent set on a unit disk graph. The method comprises the following steps: 1, designing an optimal solution solving method fora maximum vertex independent set of an adjacent vertex set induction sub-graph of unit disc vertexes by utilizing a dynamic programming method, and giving an optimal solution for a maximum vertex independent set of a union set induction sub-graph of any two vertex adjacent vertex sets; 2, for a general unit disk graph, firstly calculating a vertex dominating independent set; then independently checking members in the vertex dominated independent set, and judging whether a result can be optimized or not to obtain an intermediate solution; and finally, performing joint inspection on members in the intermediate solution, and judging whether a result can be optimized or not to obtain a final solution. According to the method, the approximate solution with the approximate ratio of 1.5 is obtained according to the calculation time complexity of O (delta 2n3), delta is the vertex maximum degree. Compared with an existing approximate algorithm for solving the problem through the maximum independent set on a unit disc graph, the approximate ratio is increased, and higher efficiency is achieved.

Description

technical field [0001] The invention belongs to the related technology of graph calculation theory, and in particular relates to an approximate solution method of the maximum independent set on a unit disk graph. Background technique [0002] UDG, or unit disk graph, is an intersection graph formed by a group of unit disks in a two-dimensional plane. It plays a vital role in modeling wireless sensor networks, mobile ad hoc networks, etc. In these networks, each node has a certain range of communication distance according to the communication protocol, and any two nodes can only communicate when they enter the communication distance of each other. If all nodes have the same communication distance, then the network can be modeled as a UDG. [0003] For the set of unit disks in the plane D={D 1 ,D 2 ,...,D n}, where D i The diameter is 1, D i The center of is the vertex v i , in all the descriptions of vertices in the present invention, it represents the center point of ...

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Problems solved by technology

Using polynomial time to solve the optimization problem on UDG still has a high time complexity

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