On the Parameterized Complexity for Token Jumping on Graphs

• Ito, Takehiro

• Kaminski, Marcin

• Ono, Hirotaka

• Suzuki, Akira

• Uehara, Ryuuhei

• Yamanaka, Katsuhisa

抄録

Suppose that we are given two independent sets Io and Ir of a graph such that |Io|=|Ir|, and imagine that a token is placed on each vertex in Io. Then, the TOKEN JUMPING problem is to determine whether there exists a sequence of independent sets which transforms Io into Ir so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between Io and Ir with the minimum number of token movements.

Theory and Applications of Models of Computation, 11th Annual Conference, TAMC 2014, Chennai, India, April 11-13, 2014. Proceedings

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/13764

収録刊行物

• Lecture Notes in Computer Science

  Lecture Notes in Computer Science 8402 341-351, 2014-04-11

  Springer

キーワード

• reconfiguration problem
• independent set
• token jumping
• PSPACE completeness
• FPT algorithm

詳細情報

• CRID: 1050845762468624128
• NII論文ID: 120005850323
• ISSN: 03029743
• ISSN: 16113349
• DOI: 10.1007/978-3-319-06089-7_24
• Web Site: http://hdl.handle.net/10119/13764
• Web Site: http://link.springer.com/content/pdf/10.1007/978-3-319-06089-7_24
• 本文言語コード: en
• 資料種別: journal article
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