An improved kernelization algorithm for r-Set Packing

We present a reduction procedure that takes an arbitrary instance of the r-Set Packing problem and produces an equivalent instance whose number of elements is in O ( k r − 1 ) , where k is the input parameter. Such parameterized reductions are known as kernelization algorithms, and a reduced instanc...

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Vydáno v:Information processing letters Ročník 110; číslo 16; s. 621 - 624
Hlavní autor: Abu-Khzam, Faisal N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 31.07.2010
Elsevier
Elsevier Sequoia S.A
Témata:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Crown decomposition
Designs and configurations
Equivalence
Exact sciences and technology
Fixed-parameter algorithms
Graph algorithms
Kernelization
Kernels
Mathematics
Miscellaneous
Packing problem
Reduction
Sciences and techniques of general use
Set Packing
Studies
Theoretical computing
Crown decomposition
Fixed-parameter algorithms
Graph algorithms
Set Packing
Kernelization
Computer theory
Decomposition method
Input
Packing
Information processing
Procedure
Algorithm analysis
Graph algorithm
ISSN:0020-0190, 1872-6119
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Popis
Shrnutí:We present a reduction procedure that takes an arbitrary instance of the r-Set Packing problem and produces an equivalent instance whose number of elements is in O ( k r − 1 ) , where k is the input parameter. Such parameterized reductions are known as kernelization algorithms, and a reduced instance is called a problem kernel. Our result improves on previously known kernelizations by a factor of k. In particular, the number of elements in a 3-Set Packing kernel is improved from a cubic function of the parameter to a quadratic one.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2010.04.020