Generation of polynomial-time algorithms for some optimization problems on 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. This paper develops new general approaches to obtain two new families of related polynomial-time algorithms for (1) packing, partitioning, and covering problems and (2) multiset and multiproperty problems. These problems have not been handled by previous general approaches.