Even Faster Algorithm for Set Splitting!

Lokshtanov, Daniel; Saurabh, Saket

doi:10.1007/978-3-642-11269-0_24

Cited by 12 publications

(10 citation statements)

References 18 publications

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“…see Chang et al [4]), and several recent algorithms for solving SSP have been developed (e.g. see Dehne et al [7], Chen and Lu [5], Lokshtanov and Saurabh [13]).…”

Section: Introductionmentioning

confidence: 99%

A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem

Haythorpe

Filar

2014

Intelligent Systems, Control and Automation: Science and Engineering

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We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it is shown that the input size of the converted instance is a linear function of the input size of the original instance. A proof that the two instances are equivalent is given, and a procedure for identifying a solution to the original instance from a solution of the converted instance is also provided. We conclude with two examples of set splitting problem instances, one with solutions and one without, and display the corresponding instances of the directed Hamiltonian cycle problem, along with a solution in the first example.

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“…see Chang et al [4]), and several recent algorithms for solving SSP have been developed (e.g. see Dehne et al [7], Chen and Lu [5], Lokshtanov and Saurabh [13]).…”

Section: Introductionmentioning

confidence: 99%

A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem

Haythorpe

Filar

2014

Intelligent Systems, Control and Automation: Science and Engineering

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“…While many problems on graphs are known to have polynomial kernels (parameterized by the solution size), there are not so many O(k), or linear-vertex kernels known in the literature. Notable examples include a 2k-vertex kernel for Vertex Cover [2], a k-vertex kernel for Set Splitting [9], and a 6k-vertex kernel for Cluster Editing [7].…”

Section: Introductionmentioning

confidence: 99%

A Linear Vertex Kernel for Maximum Internal Spanning Tree

Fomin

Gaspers

Saurabh

et al. 2009

Algorithms and Computation

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Abstract. We present a polynomial time algorithm that for any graph G and integer k ≥ 0, either nds a spanning tree with at least k internal vertices, or outputs a new graph GR on at most 3k vertices and an integer k such that G has a spanning tree with at least k internal vertices if and only if GR has a spanning tree with at least k internal vertices. In other words, we show that the Maximum Internal Spanning Tree problem parameterized by the number of internal vertices k, has a 3k-vertex kernel. Our result is based on an innovative application of a classical min-max result about hypertrees in hypergraphs which states that a hypergraph H contains a hypertree if and only if H is partition connected.

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“…While many problems on graphs are known to have polynomial kernels (parameterized by the solution size), there are not so many O (k), or linearvertex kernels known in the literature. Notable examples include a 2k-vertex kernel for Vertex Cover [2], a k-vertex kernel for Set Splitting [9], and a 6k-vertex kernel for Cluster Editing [7].…”

mentioning

confidence: 99%

A linear vertex kernel for maximum internal spanning tree

Fomin

Gaspers

Saurabh

et al. 2013

Journal of Computer and System Sciences

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We present a polynomial time algorithm that for any graph G and integer k 0, either finds a spanning tree with at least k internal vertices, or outputs a new graph G R on at most 3k vertices and an integer k such that G has a spanning tree with at least k internal vertices if and only if G R has a spanning tree with at least k internal vertices. In other words, we show that the Maximum Internal Spanning Tree problem parameterized by the number of internal vertices k has a 3k-vertex kernel. Our result is based on an innovative application of a classical min-max result about hypertrees in hypergraphs which states that "a hypergraph H contains a hypertree if and only if H is partition-connected."

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Even Faster Algorithm for Set Splitting!

Cited by 12 publications

References 18 publications

A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem

A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem

A Linear Vertex Kernel for Maximum Internal Spanning Tree

A linear vertex kernel for maximum internal spanning tree

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