Years and Authors of Summarized Original Work
-
2010; Dell, van Melkebeek
Problem Definition
The work of Dell and van Melkebeek [4] refines the framework for lower bounds for kernelization introduced by Bodlaender et al. [1] and Fortnow and Santhanam [6]. The main contribution is that their results yield a framework for proving polynomial lower bounds for kernelization rather than ruling out all polynomial kernels for a problem; this, for the first time, gives a technique for proving that some polynomial kernelizations are actually best possible, modulo reasonable complexity assumptions. A further important aspect is that, rather than studying kernelization directly, the authors give lower bounds for a far more general oracle communication protocol. In this way, they also obtain strong lower bounds for sparsification, lossy compression (in the sense of Harnik and Naor [7]), and probabilistically checkable proofs (PCPs).
oracle communication protocols, let us first recall the following. A
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Bodlaender HL, Downey RG, Fellows MR, Hermelin D (2009) On problems without polynomial kernels. J Comput Syst Sci 75(8):423–434
Cygan M, Grandoni F, Hermelin D (2013) Tight kernel bounds for problems on graphs with small degeneracy – (extended abstract). In: Bodlaender HL, Italiano GF (eds) ESA. Lecture notes in computer science, vol 8125. Springer, pp 361–372
Dell H, Marx D (2012) Kernelization of packing problems. In: SODA, Kyoto. SIAM, pp 68–81
Dell H, van Melkebeek D (2010) Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses. In: Schulman LJ (ed) STOC, Cambridge. ACM, pp 251–260
Dell H, van Melkebeek D (2010) Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses. Electron Colloq Comput Complex 17:38
Fortnow L, Santhanam R (2011) Infeasibility of instance compression and succinct PCPs for NP. J Comput Syst Sci 77(1):91–106
Harnik D, Naor M (2010) On the compressibility of \(\mathcal{N}\mathcal{P}\) instances and cryptographic applications. SIAM J Comput 39(5):1667–1713
Hermelin D, Wu X (2012) Weak compositions and their applications to polynomial lower bounds for kernelization. In: SODA, Kyoto. SIAM, pp 104–113
Kratsch S (2012) Co-nondeterminism in compositions: a kernelization lower bound for a Ramsey-type problem. In: SODA, Kyoto. SIAM, pp 114–122
Kratsch S, Pilipczuk M, Rai A, Raman V (2012) Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs. In: Fomin FV, Kaski P (eds) SWAT, Helsinki. Lecture notes in computer science, vol 7357. Springer, pp 364–375
Kratsch S, Philip G, Ray S (2014) Point line cover: the easy kernel is essentially tight. In: SODA, Portland. SIAM, pp 1596–1606
Thomassé S (2010) A quadratic kernel for feedback vertex set. ACM Trans Algorithms 6(2), 32:1–32:8
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
Kratsch, S. (2016). Kernelization, Polynomial Lower Bounds. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_522
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2864-4_522
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2863-7
Online ISBN: 978-1-4939-2864-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering