NDLI: Lossy kernelization

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Lossy kernelization

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Lossy kernelization

Content Provider	ACM Digital Library
Author	Panolan, Fahad Ramanujan, M. S. Lokshtanov, Daniel Saurabh, Saket
Abstract	In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of kernelization, our definitions com- bine well with approximation algorithms and heuristics. The key new definition is that of a polynomial size Î±-approximate kernel. Loosely speaking, a polynomial size Î±-approximate kernel is a polynomial time pre-processing algorithm that takes as input an instance (I, k) to a parameterized problem, and outputs another instance (Iâ ²,kâ ²) to the same problem, such that \|Iâ ²\| + kâ ² â ¤ $k^{O(1)}.$ Additionally, for every câ ¥ 1, a c-approximate solution sâ ² to the pre-processed instance (Iâ ², kâ ²) can be turned in polynomial time into a (c Â· Î±)-approximate solution s to the original instance (I,k). Amongst our main technical contributions are Î±-approximate kernels of polynomial size for three problems, namely Connected Vertex Cover, Disjoint Cycle Packing and Disjoint Factors. These problems are known not to admit any polynomial size kernels unless NPâ coNP/Poly. Our approximate kernels simultaneously beat both the lower bounds on the (normal) kernel size, and the hardness of approximation lower bounds for all three problems. On the negative side we prove that Longest Path parameterized by the length of the path and Set Cover parameterized by the universe size do not admit even an Î±-approximate kernel of polynomial size, for any Î±â ¥ 1, unless NP â coNP/Poly. In order to prove this lower bound we need to combine in a non-trivial way the techniques used for showing kernelization lower bounds with the methods for showing hardness of approximation. .
Starting Page	224
Ending Page	237
Page Count	14
File Format	PDF
ISBN	9781450345286
DOI	10.1145/3055399.3055456
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-06-19
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Inapproximability Parameterized complexity Kernelization
Content Type	Text
Resource Type	Article

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