Parameterized Complexity of Graph Burning

Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterize...

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Vydáno v:	Algorithmica Ročník 84; číslo 8; s. 2379 - 2393
Hlavní autoři:	Kobayashi, Yasuaki, Otachi, Yota
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2022 Springer Nature B.V
Témata:	Algorithm Analysis and Problem Complexity Algorithms Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Parameterization Parameters Polynomials Special Issue: Parameterized and Exact Computation (IPEC 2020) Theory of Computation Fixed-parameter tractability Parameterized complexity Graph burning
ISSN:	0178-4617, 1432-0541
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Abstract	Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions by Kare and Reddy [IWOCA 2019] about the parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP / poly . We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Using a different technique, we show that parameterization by distance to split graphs is also tractable. We finally show that the problem parameterized by max leaf number is XP.
AbstractList	Graph Burning asks, given a graph $$G = (V,E)$$ G = ( V , E ) and an integer k , whether there exists $$(b_{0},\dots ,b_{k-1}) \in V^{k}$$ ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some $$b_{i}$$ b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions by Kare and Reddy [IWOCA 2019] about the parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless $$\mathrm {NP} \subseteq \mathrm {coNP/poly}$$ NP ⊆ coNP / poly . We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Using a different technique, we show that parameterization by distance to split graphs is also tractable. We finally show that the problem parameterized by max leaf number is XP. Graph Burning asks, given a graph G=(V,E) and an integer k, whether there exists (b0,⋯,bk-1)∈Vk such that every vertex in G has distance at most i from some bi. This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions by Kare and Reddy [IWOCA 2019] about the parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP⊆coNP/poly. We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Using a different technique, we show that parameterization by distance to split graphs is also tractable. We finally show that the problem parameterized by max leaf number is XP. Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions by Kare and Reddy [IWOCA 2019] about the parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP / poly . We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Using a different technique, we show that parameterization by distance to split graphs is also tractable. We finally show that the problem parameterized by max leaf number is XP.
Author	Kobayashi, Yasuaki Otachi, Yota
Author_xml	– sequence: 1 givenname: Yasuaki surname: Kobayashi fullname: Kobayashi, Yasuaki organization: Hokkaido University – sequence: 2 givenname: Yota orcidid: 0000-0002-0087-853X surname: Otachi fullname: Otachi, Yota email: otachi@nagoya-u.jp organization: Nagoya University
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Cites_doi	10.11575/cdm.v16i1.71194 10.1016/j.dam.2017.09.012 10.1016/j.amc.2019.05.031 10.1137/0405010 10.1137/S0097539701385351 10.1007/s40840-020-00969-w 10.1007/s002249910009 10.1007/978-3-642-27875-4 10.1016/j.dam.2020.03.062 10.1145/1435375.1435385 10.1137/0404010 10.1007/978-3-319-21275-3 10.1016/j.dam.2017.07.016 10.1137/S0097539792228228 10.1007/s00373-020-02182-9 10.1016/0166-218X(92)90121-P 10.1016/0020-0190(94)00105-7 10.1007/s00373-021-02390-x 10.1016/j.tcs.2018.05.035 10.1080/15427951.2015.1103339 10.1016/j.tcs.2011.04.039 10.1007/s00224-016-9685-1 10.1016/j.amc.2020.125447 10.1016/j.tcs.2018.06.036 10.1145/3051095 10.1109/12.537129 10.1007/s00373-017-1768-5 10.1145/2650261 10.1007/978-3-030-25005-8_25 10.1007/978-3-319-13123-8_2 10.1007/978-3-030-68211-8_22 10.1007/978-1-4612-0515-9 10.1002/(SICI)1097-0037(199603)27:2<145::AID-NET6>3.0.CO;2-K 10.1007/978-3-319-03898-8_15 10.1007/978-3-540-30559-0_21 10.1007/978-3-030-63072-0_12 10.1007/978-3-319-49787-7_1 10.20429/tag.2020.070108 10.1007/978-3-030-38919-2_10 10.1007/978-3-319-74180-2_13 10.1007/978-3-030-14812-6_6
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Snippet	Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at... Graph Burning asks, given a graph $$G = (V,E)$$ G = ( V , E ) and an integer k , whether there exists $$(b_{0},\dots ,b_{k-1}) \in V^{k}$$ ( b 0 , ⋯ , b k - 1... Graph Burning asks, given a graph G=(V,E) and an integer k, whether there exists (b0,⋯,bk-1)∈Vk such that every vertex in G has distance at most i from some...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Parameterization Parameters Polynomials Special Issue: Parameterized and Exact Computation (IPEC 2020) Theory of Computation
Title	Parameterized Complexity of Graph Burning
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