On the OBDD Size for Graphs of Bounded Tree- and Clique-Width
We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function f G of a graph G on n vertices. Our results are as follows:
-) For graphs of bounded tree-width there is an OBDD of size O(logn) for f G that uses encodings of size O(logn) for the vertices;
-) For graphs of bounded clique-width there is an OBDD of size O(n) for f G that uses encodings of size O(n) for the vertices;
-) For graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(logn) there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices;
-) For cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices. This last result improves a recent result by Nunkesser and Woelfel .
KeywordsBoolean Function Tree Decomposition Binary Decision Diagram Adjacency List Discrete Apply Mathematic
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