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An algorithmic study of switch graphs

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Abstract

We derive a variety of results on the algorithmics of switch graphs. On the negative side we prove hardness of the following problems: Given a switch graph, does it possess a bipartite/planar/triangle-free/Eulerian configuration? On the positive side we design fast algorithms for several connectivity problems in undirected switch graphs, and for recognizing acyclic configurations in directed switch graphs.

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References

  1. Cook M.: In: Moore, C., Griffeath, D. (eds) New Constructions in Cellular Automata, Volume 226, pp. 93–118. Oxford University Press, Oxford (2003)

    Google Scholar 

  2. Cornuéjols G.: General factors of graphs. J. Comb. Theory Ser. B 45, 185–198 (1988)

    Article  MATH  Google Scholar 

  3. de Berg, M., Khosravi, A.: Optimal binary space partitions in the plane. In: Proceeding of 16th International Computing and Combinatorics Conference (COCOON’2010), vol. 6196 of LNCS, pp. 216–225. Springer, Berlin (2010)

  4. Edmonds, J.: Submodular functions, matroids, and certain polyhedra. In: Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications, pp. 69–87. Calgary (1969)

  5. Garey M.R., Johnson D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  6. Groote J., Ploeger B.: Switching graphs. Int. J. Found. Comput. Sci. 20(5), 869–886 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hall P.: On representatives of subsets. J. Lond. Math. Soc. 10, 26–30 (1935)

    Article  Google Scholar 

  8. Huckenbeck, U.: On paths in networks with valves. In: Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science (STACS’93), vol. 665 of LNCS, pp. 90–99 (1993)

  9. Huckenbeck U.: On valve adjustments that interrupt all s-t-paths in a digraph. J. Autom. Lang. Comb. 2(1), 19–45 (1997)

    MathSciNet  MATH  Google Scholar 

  10. Katz, B., Rutter, I., Woeginger, G.: An algorithmic study of switch graphs. In: Proceeding of 35th International Workshop Graph-Theoretical Concepts in Computer Science (WG’09), pp. 226–237, LNCS. Springer, Berlin

  11. Korte B., Vygen J.: Combinatorial Optimization, Theory and Algorithms. Springer, New York (2008)

    Google Scholar 

  12. Meinel, C.: Switching graphs and their complexity. In: Proceedings of the 14th Conference on Mathematical Foundations of Computer Science (MFCS’1989), vol. 379 of LNCS, pp. 350–359. Springer, Berlin (1989)

  13. Plesńik J.: The NP-completeness of the Hamiltonian cycle problem in planar digraphs with degree bound two. Inf. Process. Lett. 8(4), 199–201 (1979)

    Article  MATH  Google Scholar 

  14. Reinhardt, K.: The simple reachability problem in switch graphs. In: Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM’2009), vol. 5404 of LNCS, pp. 461–472. Springer, Berlin (2009)

  15. Sharan R., Gramm J., Yakhini Z., Ben-Dor A.: Multiplexing schemes for generic SNP genotyping assays. J. Comp. Biol. 15, 514–533 (2005)

    Article  Google Scholar 

  16. Tarjan R.E.: Data Structures and Network Algorithms. SIAM, Philadelphia (1983)

    Book  Google Scholar 

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Correspondence to Ignaz Rutter.

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A preliminary version of this work has appeared as [10].

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Katz, B., Rutter, I. & Woeginger, G. An algorithmic study of switch graphs. Acta Informatica 49, 295–312 (2012). https://doi.org/10.1007/s00236-012-0160-4

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