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Abstract

A graph G = (V,E) can be described by the characteristic function of the edge set \(\mathcal{X}_E\) which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using Ordered Binary Decision Diagrams (OBDDs) to store \(\mathcal{X}_E\) can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g., quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is O( ∣ V ∣ /log ∣ V ∣ ) and the OBDD size of interval graphs is O( ∣ V ∣ log ∣ V ∣ ) which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is Ω( ∣ V ∣ log ∣ V ∣ ). We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using O(log ∣ V ∣ ) operations and evaluate the algorithm empirically.

Keywords

Boolean Function Adjacency Matrix Variable Order Interval Graph Maximum Match 
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 Berlin Heidelberg 2013

Authors and Affiliations

  • Marc Gillé
    • 1
  1. 1.LS2 InformatikTU DortmundGermany

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