Abstract
Kernelization is a formalization of preprocessing for combinatorially hard problems. We modify the standard definition for kernelization, which allows any polynomial-time algorithm for the preprocessing, by requiring instead that the preprocessing runs in a streaming setting and uses \(\mathcal{O}(poly(k)\log|x|)\) bits of memory on instances (x,k). We obtain several results in this new setting, depending on the number of passes over the input that such a streaming kernelization is allowed to make. Edge Dominating Set turns out as an interesting example because it has no single-pass kernelization but two passes over the input suffice to match the bounds of the best standard kernelization.
Supported by the Emmy Noether-program of the DFG, KR 4286/1.
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References
Arora, S., Barak, B.: Computational complexity: a modern approach. Cambridge University Press (2009)
Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: PODS, pp. 1–16. ACM (2002)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer (2013)
Erdös, P., Rado, R.: Intersection theorems for systems of sets. Journal of the London Mathematical Society 1(1), 85–90 (1960)
Fafianie, S., Kratsch, S.: Streaming kernelization. arXiv report 1405.1356 (2014)
Fellows, M.R., Jansen, B.M.P., Rosamond, F.A.: Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity. Eur. J. Comb. 34(3), 541–566 (2013)
Hagerup, T.: Simpler Linear-Time Kernelization for Planar Dominating Set. In: Marx, D., Rossmanith, P. (eds.) IPEC 2011. LNCS, vol. 7112, pp. 181–193. Springer, Heidelberg (2012)
Henzinger, M.R., Raghavan, P., Rajagopalan, S.: Computing on data streams. In: External Memory Algorithms: DIMACS Workshop External Memory and Visualization, May 20-22, vol. 50, p. 107. AMS (1999)
Kammer, F.: A Linear-Time Kernelization for the Rooted k-Leaf Outbranching Problem. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds.) WG 2013. LNCS, vol. 8165, pp. 310–320. Springer, Heidelberg (2013)
Lokshtanov, D., Misra, N., Saurabh, S.: Kernelization – Preprocessing with a Guarantee. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift 2012. LNCS, vol. 7370, pp. 129–161. Springer, Heidelberg (2012)
Misra, N., Raman, V., Saurabh, S.: Lower bounds on kernelization. Discrete Optimization 8(1), 110–128 (2011)
Muthukrishnan, S.: Data streams: Algorithms and applications. Now Publishers Inc. (2005)
van Bevern, R.: Towards Optimal and Expressive Kernelization for d-Hitting Set. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 121–132. Springer, Heidelberg (2012)
van Bevern, R., Hartung, S., Kammer, F., Niedermeier, R., Weller, M.: Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs. In: Marx, D., Rossmanith, P. (eds.) IPEC 2011. LNCS, vol. 7112, pp. 194–206. Springer, Heidelberg (2012)
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Fafianie, S., Kratsch, S. (2014). Streaming Kernelization. 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_24
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DOI: https://doi.org/10.1007/978-3-662-44465-8_24
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