TY - CHAP
T1 - A Retrospective on (Meta) Kernelization
AU - Thilikos, Dimitrios M.
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - In parameterized complexity, a kernelization algorithm can be seen as a reduction of a parameterized problem to itself, so that the produced equivalent instance has size depending exclusively on the parameter. If this size is polynomial, then we say that the parameterized problem in question admits a polynomial kernelization algorithm. Kernelization can be seen as a formalization of the notion of preprocessing and has occupied a big part of the research on Multi-variate Algorithmics. The first algorithmic meta-theorem on kernelization appeared in [14] and unified a large family of previously known kernelization results on problems defined on topologically embeddable graphs. In this exposition we present the central results of this paper. During our presentation we pay attention to the abstractions on which the results where founded and take into account the subsequent advancements on this topic.
AB - In parameterized complexity, a kernelization algorithm can be seen as a reduction of a parameterized problem to itself, so that the produced equivalent instance has size depending exclusively on the parameter. If this size is polynomial, then we say that the parameterized problem in question admits a polynomial kernelization algorithm. Kernelization can be seen as a formalization of the notion of preprocessing and has occupied a big part of the research on Multi-variate Algorithmics. The first algorithmic meta-theorem on kernelization appeared in [14] and unified a large family of previously known kernelization results on problems defined on topologically embeddable graphs. In this exposition we present the central results of this paper. During our presentation we pay attention to the abstractions on which the results where founded and take into account the subsequent advancements on this topic.
KW - Algorithmic meta-theorems finite index
KW - Bidimensionality
KW - Finite integer index
KW - Kernelization algorithms
KW - Monadic Second Order Logic
KW - Parameterized algorithms
KW - Parameterized problems
KW - Protrusion decompositions
KW - Separability
KW - Treewidth
UR - http://www.scopus.com/inward/record.url?scp=85090001859&partnerID=8YFLogxK
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U2 - 10.1007/978-3-030-42071-0_16
DO - 10.1007/978-3-030-42071-0_16
M3 - Chapter
AN - SCOPUS:85090001859
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 222
EP - 246
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PB - Springer
ER -