Sequential and parallel algorithms for embedding problems on classes of partial k-trees

Abstract

We present sequential and parallel algorithms for various embedding problems on bounded degree partial k-trees and k-connected partial k-trees; these include subgraph isomorphism and topological embedding, known to be NP-complete for general partial k-trees. As well as contributing to our understanding of the types of graphs for which these problems are tractable, this paper introduces new methods for solving problems on graphs. In particular, we make use of a tree-like representation of the graph (the tree-decomposition of the graph) to apply techniques used to solve problems on trees to solve problems on more general classes of graphs,