Parameterized Complexity of the Firefighter Problem
Identifieur interne : 001518 ( Istex/Corpus ); précédent : 001517; suivant : 001519Parameterized Complexity of the Firefighter Problem
Auteurs : Cristina Bazgan ; Morgan Chopin ; Michael R. FellowsSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2011.
English descriptors
- KwdEn :
- Algorithm, Bipartite graphs, Busy gadget, Busy gadgets, Clique, Computable function, Cubic graphs, Discrete mathematics, Equivalent instance, Former problem, General graphs, Heidelberg, Input instance, Kernel, Maximum degree, Output instance, Parameter tractability, Parameterized, Parameterized complexity, Parameterized intractability, Parameterized problem, Parameterized problems, Planar graphs, Poly kernel, Polynomial kernel, Polynomial kernels, Polynomial time, Problem parameterized, Protection strategy, Reduction rule, Regular clique, Same number, Several cases, Subset, Time proof, Time step, Tractable, Valid strategy, Vertex, Vulnerable vertex.
- Teeft :
- Algorithm, Bipartite graphs, Busy gadget, Busy gadgets, Clique, Computable function, Cubic graphs, Discrete mathematics, Equivalent instance, Former problem, General graphs, Heidelberg, Input instance, Kernel, Maximum degree, Output instance, Parameter tractability, Parameterized, Parameterized complexity, Parameterized intractability, Parameterized problem, Parameterized problems, Planar graphs, Poly kernel, Polynomial kernel, Polynomial kernels, Polynomial time, Problem parameterized, Protection strategy, Reduction rule, Regular clique, Same number, Several cases, Subset, Time proof, Time step, Tractable, Valid strategy, Vertex, Vulnerable vertex.
Abstract
Abstract: In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that Saving k -Vertices and its dual Saving All But k -Vertices are both W[1]-hard for parameter k even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, Saving k -Vertices is fixed-parameter tractable on planar graphs for parameter k. Moreover, we prove a lower bound to polynomial kernelization for Saving All But k -Vertices.
Url:
DOI: 10.1007/978-3-642-25591-5_66
Links to Exploration step
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<abstract xml:lang="en"><p>Abstract: In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that Saving k -Vertices and its dual Saving All But k -Vertices are both W[1]-hard for parameter k even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, Saving k -Vertices is fixed-parameter tractable on planar graphs for parameter k. Moreover, we prove a lower bound to polynomial kernelization for Saving All But k -Vertices.</p>
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<Para>In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that <Emphasis Type="SmallCaps">Saving </Emphasis>
<Emphasis Type="Italic">k</Emphasis>
<Emphasis Type="SmallCaps">-Vertices</Emphasis>
and its dual <Emphasis Type="SmallCaps">Saving All But </Emphasis>
<Emphasis Type="Italic">k</Emphasis>
<Emphasis Type="SmallCaps">-Vertices</Emphasis>
are both W[1]-hard for parameter <Emphasis Type="Italic">k</Emphasis>
even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, <Emphasis Type="SmallCaps">Saving </Emphasis>
<Emphasis Type="Italic">k</Emphasis>
<Emphasis Type="SmallCaps">-Vertices</Emphasis>
is fixed-parameter tractable on planar graphs for parameter <Emphasis Type="Italic">k</Emphasis>
. Moreover, we prove a lower bound to polynomial kernelization for <Emphasis Type="SmallCaps">Saving All But </Emphasis>
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<abstract lang="en">Abstract: In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that Saving k -Vertices and its dual Saving All But k -Vertices are both W[1]-hard for parameter k even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, Saving k -Vertices is fixed-parameter tractable on planar graphs for parameter k. Moreover, we prove a lower bound to polynomial kernelization for Saving All But k -Vertices.</abstract>
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