Distributed tree decomposition of graphs and applications to verification

The tree decomposition of graphs is a fundamental algorithmic tool. It has been shown that difficult problems, such as some NP-complete ones, can be solved efficiently over classes of graphs of bounded tree-width. We consider in this paper the distributed construction of the tree decompositions of network topology graphs. We propose algorithms to distributively construct the tree-decomposition of respectively (i) planar networks of bounded diameter and (ii) networks of bounded degree and bounded tree-length. Both algorithms are very efficient, requiring only a constant number of messages sent over each link. We then use these algorithms to distributively verify properties of graphs expressible in Monadic Second Order Logic, MSO.