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On the boolean-width of a graph: structure and applications I. Adler1 , B.-M. Bui-Xuan1 , Y. Rabinovich2 , G. Renault1 , J. A. Telle1 , and M. Vatshelle1
 

Summary: On the boolean-width of a graph: structure and applications
I. Adler1 , B.-M. Bui-Xuan1 , Y. Rabinovich2 , G. Renault1 , J. A. Telle1 , and M. Vatshelle1
1
Department of Informatics, University of Bergen, Norway
2
Department of Computer Science, Haifa University, Israel
Abstract Boolean-width is a recently introduced graph invariant. Similar to tree-width, it mea-
sures the structural complexity of graphs. Given any graph G and a decomposition of G of boolean-
width k, we give algorithms solving a large class of vertex subset and vertex partitioning problems
in time O
(2O(k2
)
). We relate the boolean-width of a graph to its branch-width and to the boolean-
width of its incidence graph. For this we use a constructive proof method that also allows much
simpler proofs of similar results on rank-width by Oum (JGT 2008). For a random graph on n
vertices we show that almost surely its boolean-width is (log2
n) ­ setting boolean-width apart
from other graph invariants ­ and it is easy to find a decomposition witnessing this. Combining
our results gives algorithms that on input a random graph on n vertices will solve a large class of
vertex subset and vertex partitioning problems in quasi-polynomial time O

  

Source: Adler, Isolde - Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt am Main

 

Collections: Computer Technologies and Information Sciences