TY - GEN
T1 - Incremental Optimization of Independent Sets Under the Reconfiguration Framework
AU - Ito, Takehiro
AU - Mizuta, Haruka
AU - Nishimura, Naomi
AU - Suzuki, Akira
N1 - Funding Information:
Research by the first, second and fourth authors is partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636, JP18H04091, JP19J10042 and JP19K11814, Japan. Research by Naomi Nishimura is partially supported by the Natural Science and Engineering Research Council of Canada.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - Suppose that we are given an independent set I0 of a graph G, and an integer (forumala presented). Then, we are asked to find an independent set of G having the maximum size among independent sets that are reachable from I0 by either adding or removing a single vertex at a time such that all intermediate independent sets are of size at least l. We show that this problem is PSPACE-hard even for bounded pathwidth graphs, and remains NP-hard for planar graphs. On the other hand, we give a linear-time algorithm to solve the problem for chordal graphs. We also study the parameterized complexity of the problem with respect to the following three parameters: the degeneracy d of an input graph, a lower bound l on the size of independent sets, and a lower bound s on the size of a solution reachable from I0. We show that the problem is fixed-parameter intractable when only one of d,l, and s is taken as a parameter. On the other hand, we give a fixed-parameter algorithm when parameterized by s+d this result implies that the problem parameterized only by s is fixed-parameter tractable for planar graphs, and for bounded treewidth graphs.
AB - Suppose that we are given an independent set I0 of a graph G, and an integer (forumala presented). Then, we are asked to find an independent set of G having the maximum size among independent sets that are reachable from I0 by either adding or removing a single vertex at a time such that all intermediate independent sets are of size at least l. We show that this problem is PSPACE-hard even for bounded pathwidth graphs, and remains NP-hard for planar graphs. On the other hand, we give a linear-time algorithm to solve the problem for chordal graphs. We also study the parameterized complexity of the problem with respect to the following three parameters: the degeneracy d of an input graph, a lower bound l on the size of independent sets, and a lower bound s on the size of a solution reachable from I0. We show that the problem is fixed-parameter intractable when only one of d,l, and s is taken as a parameter. On the other hand, we give a fixed-parameter algorithm when parameterized by s+d this result implies that the problem parameterized only by s is fixed-parameter tractable for planar graphs, and for bounded treewidth graphs.
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U2 - 10.1007/978-3-030-26176-4_26
DO - 10.1007/978-3-030-26176-4_26
M3 - Conference contribution
AN - SCOPUS:85070192144
SN - 9783030261757
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 313
EP - 324
BT - Computing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings
A2 - Du, Ding-Zhu
A2 - Duan, Zhenhua
A2 - Tian, Cong
PB - Springer Verlag
T2 - 25th International Computing and Combinatorics Conference, COCOON 2019
Y2 - 29 July 2019 through 31 July 2019
ER -