TY - GEN

T1 - Approximating Partially Bounded Degree Deletion on Directed Graphs

AU - Fujito, Toshihiro

AU - Kimura, Kei

AU - Mizuno, Yuki

N1 - Funding Information:
This work is supported in part by JSPS KAKENHI under Grant Numbers 26330010 and 17K00013.
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.

UR - http://www.scopus.com/inward/record.url?scp=85043341826&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043341826&partnerID=8YFLogxK

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 -