A Linear-Time Kernelization for the Rooted k-Leaf Outbranching Problem

Kammer, Frank

doi:10.1007/978-3-642-45043-3_27

Cited by 6 publications

(3 citation statements)

References 12 publications

(24 reference statements)

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“…We show that a problem kernel for d-Hitting Set with O(k d ) hyperedges and vertices is computable in linear time. Thereby, we prove the previously claimed result by Niedermeier and Rossmanith [30] and complement recent results in improving the efficiency of kernelization algorithms [5,15,21,22,33].…”

Section: Introductionsupporting

confidence: 87%

Towards Optimal and Expressive Kernelization for d-Hitting Set

Bevern

2012

Lecture Notes in Computer Science

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d-HittingSet is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example, fault diagnosis, automatic program verification, and the noise-minimizing assignment of frequencies to radio transmitters.We show a linear-time algorithm that transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k d ) hyperedges and vertices. In terms of parameterized complexity, this is a problem kernel. Our kernelization algorithm is based on speeding up the wellknown approach of finding and shrinking sunflowers in hypergraphs, which yields problem kernels with structural properties that we condense into the concept of expressive kernelization.We conduct experiments to show that our kernelization algorithm can kernelize instances with more than 10 7 hyperedges in less than five minutes.Finally, we show that the number of vertices in the problem kernel can be further reduced to O(k d−1 ) with additional O(k 1.5d ) processing time by nontrivially combining the sunflower technique with d-Hitting Set problem kernels due to Abu-Khzam and Moser.

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Section: Introductionsupporting

confidence: 87%

Towards Optimal and Expressive Kernelization for d-Hitting Set

Bevern

2012

Lecture Notes in Computer Science

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“…This includes choice of parameter, computational complexity, and also conceptual difficulty (e.g., number of black box subroutines, huge hidden constants). Stronger parameterizations already receive substantial interest from a theoretical point of view, see e.g., [3], and there is considerable interest in making kernelizations fast, see e.g., [11,4,10,6]. Conceptual difficulty is of course "in the eye of the beholder" and perhaps hard to quantify.…”

Section: Introductionmentioning

confidence: 99%

Streaming Kernelization

Fafianie

Kratsch

2014

Mathematical Foundations of Computer Science 2014

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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 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. 1 Unless NP ⊆ coNP/poly and the polynomial hierarchy collapses.

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“…In contrast, the only linear-time kernelization known to the author is for Vertex Cover [8,9], for Bicluster Graph Editing [19] on general undirected graphs, for d-Hitting Set [2] on undirected hypergraphs, and for Feedback Vertex Set [18], Face Cover [18], and Dominating Set [3,15] on undirected planar graphs, but no linear-time kernelization on digraphs. In a preliminary version [17] of this paper, we showed a linear-time kernelization for the Rooted k-Leaf Outbranching Problem.…”

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confidence: 99%