Decomposition trees: Structured graph representation and efficient algorithms
A data structure, decomposition trees, is introduced, which enables graphs to be represented in a certain structured way, and which leads to simple, recursive algorithms for many difficult graph problems.
For a number of NP-complete problems these algorithms are shown to run in linear time on decomposition trees with bounded label size. Furthermore it is shown that for those graphs which have decomposition tree representations with bounded label size such a representation can be constructed in polynomial time.
Put together, these algorithms solve a number of NP-complete problems in polynomial time on many graph classes, including all those graph languages that can be generated by any sort of context-free graph grammars, e.g., (hyper-)edge replacement grammars.
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