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On the Width of Ordered Binary Decision Diagrams

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

Ordered binary decision diagrams (OBDDs) are a popular data structure for Boolean functions. One of its complexity measures is the width which has been investigated in several areas in computer science like machine learning, property testing, and the design and analysis of implicit graph algorithms. Maybe the most important issue of OBDDs is the possibility to choose the variable ordering and for a given function the width of an OBDD is very sensitive to this choice. The main result of the paper is the proof that the width minimization problem is NP-hard. Furthermore, two basic problems in the design and analysis of implicit graph algorithms are reinvestigated and known upper bounds on their complexity that depend on the width of the input OBDDs are improved.

The author is supported by DFG project BO 2755/1-2.

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References

  1. Bollig, B.: On symbolic OBDD-based algorithms for the minimum spanning tree problem. Theor. Comput. Sci. 447, 2–12 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bollig, B.: On the complexity of some ordering problems. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014, Part II. LNCS, vol. 8635, pp. 118–129. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Bollig, B., Gillé, M., Pröger, T.: Implicit computation of maximum bipartite matchings by sublinear functional operations. Theor. Comput. Sci. (2014). doi:10.1016/j.tcs.2014.07.020

  4. Bollig, B., Löbbing, M., Wegener, I.: On the effect of local changes in the variable ordering of ordered decision diagrams. Inf. Process. Lett. 59, 233–239 (1996)

    Article  MATH  Google Scholar 

  5. Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. Comput. 45(9), 993–1002 (1996)

    Article  MATH  Google Scholar 

  6. Brody, J., Matulef, K., Wu, C.: Lower bounds for testing computability by small width OBDDs. In: Ogihara, M., Tarui, J. (eds.) TAMC 2011. LNCS, vol. 6648, pp. 320–331. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Bryant, R.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  8. Ergün, F., Kumar, R., Rubinfeld, R.: On learning bounded-width branching programs. In: Mass, W. (ed.) COLT, pp. 361–368. ACM (1995)

    Google Scholar 

  9. Fortune, F., Hopcroft, J., Schmidt, E.M.: The complexity of equivalence and containment for free single variable program schemes. In: Ausiello, G., Böhm, C. (eds.) ICALP 1978. LNCS, vol. 62, pp. 227–240. Springer, Heidelberg (1978)

    Chapter  Google Scholar 

  10. Gavril, F.: Some NP-complete problems on graphs. In: 11th Conference on Information Science and Systems, pp. 91–95 (1977)

    Google Scholar 

  11. Goldreich, O.: On testing computability by small width OBDDs. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX 2010. LNCS, vol. 6302, pp. 574–587. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Hachtel, G., Somenzi, F.: A symbolic algorithm for maximum flow in \(0\)-\(1\) networks. Form. Meth. Syst. Des. 10, 207–219 (1997)

    Article  Google Scholar 

  13. Newman, I.: Testing membership in languages that have small width branching programs. SIAM J. Comput. 31(5), 1557–1570 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ron, D., Tsur, G.: Testing computability by width-two OBDDs. Theor. Comput. Sci. 420, 64–79 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Savický, P., Wegener, I.: Efficient algorithms for the transformation between different types of binary decision diagrams. Acta Informatica 34(4), 245–256 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Sawitzki, D.: Implicit flow maximization by iterative squaring. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2004. LNCS, vol. 2932, pp. 301–313. Springer, Heidelberg (2004)

    Google Scholar 

  17. Sawitzki, D.: A symbolic approach to the all-pairs shortest-paths problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 154–167. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Sawitzki, D.: The complexity of problems on implicitly represented inputs. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 471–482. Springer, Heidelberg (2006)

    Google Scholar 

  19. Sawitzki, D.: Exponential lower bounds on the space complexity of OBDD-based graph algorithms. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 781–792. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Sieling, D., Wegener, I.: NC-algorithms for operations on binary decision diagrams. Parallel Process. Lett. 3, 3–12 (1993)

    Article  MathSciNet  Google Scholar 

  21. Wegener, I.: Branching programs and binary decision diagrams: theory and applications. SIAM, Philadelphia (2000)

    Google Scholar 

  22. Woelfel, P.: Symbolic topological sorting with OBDDs. J. Discrete Algorithm 4(1), 51–71 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgment

The author would like to thank the referees for comments which helped to improve the presentation of the paper.

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Authors and Affiliations

  1. LS2 Informatik, TU Dortmund, Dortmund, Germany

    Beate Bollig

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  1. Beate Bollig
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Correspondence to Beate Bollig .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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Bollig, B. (2014). On the Width of Ordered Binary Decision Diagrams. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_33

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

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