Abstract: Tree width and tree decomposition arc two important concepts developed by graph minor theory. Because of its own characteristics, tree decomposition plays an important role in algorithm design. The tree width of graph, tree decomposition algorithm, applications of tree decomposition algorithm for problem solving in a complex problems were deeply analysed. Three aspects of the related research in recent years were given a thorough analysis and presentation,and a number of important principles and methods were presented by some simple examples. Furthermore, a few future research issues were outlined.

Key words: Graph minor, Tree width, Tree decomposition, Parameterized algorithm, Approximation algorithm