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Parameterized Complexity of Graph Burning
| Title: | Parameterized Complexity of Graph Burning |
| Authors: | Kobayashi, Yasuaki Browse this author →KAKEN DB | | Otachi, Yota Browse this author |
| Keywords: | Graph burning | | Parameterized complexity | | Fixed-parameter tractability |
| Issue Date: | 19-Jul-2022 |
| Publisher: | Springer |
| Journal Title: | Algorithmica |
| Volume: | 84 |
| Start Page: | 2379 |
| End Page: | 2393 |
| Publisher DOI: | 10.1007/s00453-022-00962-8 |
| Abstract: | GRAPH BURNING asks, given a graph G = (V, E) and an integer k, whether there exists (b(0), ...,b(k-1)) is an element of 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 subset of 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. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/86314 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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