On polynomial time algorithms for tree-decomposable graphs

Recent work in the design of efficient algorithms for optimization problems on tree-decomposable graphs concentrates on developing general approaches which lead to families of related algorithms, rather than on developing isolated ad hoc algorithms. The author extends previous results to obtain novel classes of related polynomial time algorithms for problems not previously handled by any general approach. Two families of polynomial time algorithms are presented for packing, partitioning, and covering problems, and for multiset and multiproperty problems