TY - GEN
T1 - Approximating Partially Bounded Degree Deletion on Directed Graphs
AU - Fujito, Toshihiro
AU - Kimura, Kei
AU - Mizuno, Yuki
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018
Y1 - 2018
N2 - The Bounded Degree Deletion problem (BDD) is that of computing a minimum vertex set in a graph G=(V,E) with degree bound b: V=Z+, such that, when it is removed from G, the degree of any remaining vertex v is no larger than b(v). It is a classic problem in graph theory and various results have been obtained including an approximation ratio of 2+In bmax [30], where bmax is the maximum degree bound. This paper considers BDD on directed graphs containing unbounded vertices, which we call Partially Bounded Degree Deletion (PBDD). Despite such a natural generalization of standard BDD, it appears that PBDD has never been studied and no algorithmic results are known, approximation or parameterized. It will be shown that (1) in case all the possible degrees are bounded, in-degrees by and out-degrees by, BDD on directed graphs can be approximated within, and (2) although it becomes NP-hard to approximate PBDD better than bmax (even on undirected graphs) once unbounded vertices are allowed, it can be within when only in-degrees (and none of out-degrees) are partially bounded by b.
AB - The Bounded Degree Deletion problem (BDD) is that of computing a minimum vertex set in a graph G=(V,E) with degree bound b: V=Z+, such that, when it is removed from G, the degree of any remaining vertex v is no larger than b(v). It is a classic problem in graph theory and various results have been obtained including an approximation ratio of 2+In bmax [30], where bmax is the maximum degree bound. This paper considers BDD on directed graphs containing unbounded vertices, which we call Partially Bounded Degree Deletion (PBDD). Despite such a natural generalization of standard BDD, it appears that PBDD has never been studied and no algorithmic results are known, approximation or parameterized. It will be shown that (1) in case all the possible degrees are bounded, in-degrees by and out-degrees by, BDD on directed graphs can be approximated within, and (2) although it becomes NP-hard to approximate PBDD better than bmax (even on undirected graphs) once unbounded vertices are allowed, it can be within when only in-degrees (and none of out-degrees) are partially bounded by b.
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U2 - 10.1007/978-3-319-75172-6_4
DO - 10.1007/978-3-319-75172-6_4
M3 - Conference contribution
AN - SCOPUS:85043341826
SN - 9783319751719
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 32
EP - 43
BT - WALCOM
A2 - Rahman, M. Sohel
A2 - Sung, Wing-Kin
A2 - Uehara, Ryuhei
PB - Springer Verlag
T2 - 12th International Conference and Workshop on Algorithms and Computation, WALCOM 2018
Y2 - 3 March 2018 through 5 March 2018
ER -