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Theory of Computing Systems

, Volume 33, Issue 2, pp 125–150 | Cite as

Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width

  • B. Courcelle
  • J. A. Makowsky
  • U. Rotics

Abstract.

Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of tree-width at most k , i.e., that have tree decompositions of width at most k , where k is fixed, every decision or optimization problem expressible in monadic second-order logic has a linear algorithm. We prove that this is also the case for graphs of clique-width at most k , where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications. We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with ``too many'' induced paths with four vertices.

Keywords

Time Solvable Linear Time Complexity Measure Tree Decomposition Logical Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • B. Courcelle
    • 1
  • J. A. Makowsky
    • 2
  • U. Rotics
    • 2
  1. 1.Laboratoire d'Informatique, Université Bordeaux-I, 33405 Talence, France Bruno.Courcelle@labri.u-bordeaux.fr FR
  2. 2.Department of Computer Science, Technion — Israel Institute of Technology, 32000 Haifa, Israel janos@cs.technion.ac.il, rotics@cs.technion.ac.ilIL

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