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 -