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On the Complexity of Some Ordering Problems

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

Two different ordering problems are investigated. Ordered binary decision diagrams (OBDDs) are a popular data structure for Boolean functions. Some applications work with a restricted variant called complete OBDDs. This model has also been investigated in complexity theory, e.g., in property testing. It is well-known that the size of an OBDD for the representation of a given function may depend significantly on the chosen variable ordering but the computation of an optimal ordering is NP-hard. Since optimal variable orderings for OBDDs are not necessarily optimal for the complete model, the complexity to find an optimal variable ordering for complete OBDDs is investigated. Here, using a new reduction idea it is shown that the problem is NP-hard. Among the many areas of applications OBDDs have been used in the design and analysis of implicit graph algorithms where the choice of a good vertex encoding is of additional importance to represent a given input graph in small size. The computational complexity of the vertex encoding problem is unknown but in the paper a first step is done to determine its complexity by showing that a restricted case is NP-hard.

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Authors and Affiliations

  1. LS2 Informatik, TU Dortmund, Germany

    Beate Bollig

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  1. Beate Bollig
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Bollig, B. (2014). On the Complexity of Some Ordering Problems. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_11

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  • DOI: https://doi.org/10.1007/978-3-662-44465-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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