TY - GEN

T1 - Approximability of the independent feedback vertex set problem for bipartite graphs

AU - Tamura, Yuma

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
T. Ito—Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. X. Zhou—Partially supported by JSPS KAKENHI Grant Number JP19K11813, Japan.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.

AB - Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.

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U2 - 10.1007/978-3-030-39881-1_24

DO - 10.1007/978-3-030-39881-1_24

M3 - Conference contribution

AN - SCOPUS:85080901203

SN - 9783030398804

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

SP - 286

EP - 295

BT - WALCOM

A2 - Rahman, M. Sohel

A2 - Sadakane, Kunihiko

A2 - Sung, Wing-Kin

PB - Springer

T2 - 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020

Y2 - 31 March 2020 through 2 April 2020

ER -