TY - GEN

T1 - On the parameterized complexity for token jumping on graphs

AU - Ito, Takehiro

AU - Kamiński, Marcin

AU - Ono, Hirotaka

AU - Suzuki, Akira

AU - Uehara, Ryuhei

AU - Yamanaka, Katsuhisa

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Suppose that we are given two independent sets I0 and I r of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 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 I0 and Ir with the minimum number of token movements.

AB - Suppose that we are given two independent sets I0 and I r of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 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 I0 and Ir with the minimum number of token movements.

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U2 - 10.1007/978-3-319-06089-7_24

DO - 10.1007/978-3-319-06089-7_24

M3 - Conference contribution

AN - SCOPUS:84958541436

SN - 9783319060880

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 341

EP - 351

BT - Theory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings

PB - Springer Verlag

T2 - 11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014

Y2 - 11 April 2014 through 13 April 2014

ER -