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
Cook M.: In: Moore, C., Griffeath, D. (eds) New Constructions in Cellular Automata, Volume 226, pp. 93–118. Oxford University Press, Oxford (2003)
Cornuéjols G.: General factors of graphs. J. Comb. Theory Ser. B 45, 185–198 (1988)
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)
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)
Garey M.R., Johnson D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979)
Groote J., Ploeger B.: Switching graphs. Int. J. Found. Comput. Sci. 20(5), 869–886 (2009)
Hall P.: On representatives of subsets. J. Lond. Math. Soc. 10, 26–30 (1935)
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)
Huckenbeck U.: On valve adjustments that interrupt all s-t-paths in a digraph. J. Autom. Lang. Comb. 2(1), 19–45 (1997)
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
Korte B., Vygen J.: Combinatorial Optimization, Theory and Algorithms. Springer, New York (2008)
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)
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)
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)
Sharan R., Gramm J., Yakhini Z., Ben-Dor A.: Multiplexing schemes for generic SNP genotyping assays. J. Comp. Biol. 15, 514–533 (2005)
Tarjan R.E.: Data Structures and Network Algorithms. SIAM, Philadelphia (1983)
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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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DOI: https://doi.org/10.1007/s00236-012-0160-4