Dynamic Programming on Graphs with Bounded Treewidth

Abstract

In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth k, (or equivalently, the class of partial k-trees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses C-LCC, and C-ECC. We show that each problem in LCC (or C-LCC) is solvable in polynomial (O(nc)) time, when restricted to graphs with fixed up-perbounds on the treewidth and degree; and that each problem in ECC (or C- ECC) is solvable in polynomial (O(n c)) time, when restricted to graphs with a fixed upperbound on the treewidth (with given corresponding tree-decomposition).