Local improving algorithms for large cuts in graphs with maximum degree three Original Research Article

We analyze ‘local switching’ search algorithms for finding large bipartite subgraphs in simple undirected graphs. The algorithms are based on the ‘measure of effectiveness’ of the partitions of the vertex set. We analyze the worst-case behaviour of these algorithms, giving general lower bounds. Using a vertex and its neighbours, we define the improving and indifferent switchings and, indexed by two numbers (m,n), procedures to improve the reading cut. Since the concept of switching has its limits, we indicate how larger the substructures should be taken to improve locally optimal solution.