Hybrid approach for graph partitioning

Abstract

The paper discusses hybrid algorithm based on the elements grouping for the graph partitioning problem which is one of the most important optimization problem in the decision making. This problem belongs to the NP-class problem that is there are no precise methods to solve this problem. Also we formulate the partitioning problem and choose an optimization criterion. The developed hybrid algorithm obtains optimal and quasi-optimal solutions during polynomial time. The distinguish feature of this algorithm is grouping of elements with the same attributes. According to aggregation mechanism, definite variety of fractals can be obtained in the process of random growth. Aggregation is a random process and creation of clusters is based on minimal arrays in graph. To compare obtained results with known analogous algorithms we developed software which allows to carry out experiments. As a result theoretical estimations of algorithm efficiency were confirmed by experimental results. The time complexity of the hybrid algorithm cam be represented as O(nlogn), O(αn3).