TY - GEN
T1 - Hitting topological minors is FPT
AU - Fomin, Fedor V.
AU - Lokshtanov, Daniel
AU - Panolan, Fahad
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© 2020 ACM.
PY - 2020/6/8
Y1 - 2020/6/8
N2 - In the Topological Minor Deletion (TM-Deletion) problem, the input consists of an undirected graph G, a family of undirected graphs F and an integer k. The task is to determine whether G contains a set of vertices S of size at most k, such that the graph Gg- S obtained from G by removing the vertices of S, contains no graph from F as a topological minor. We give an algorithm forTM-Deletion with running time f(hg,k)· |V(G)|4. Here hg is the maximum size of a graph in F and f is a computable function of hg and k. This is the first fixed parameter tractable algorithm (FPT) for the problem. In fact, even for the restricted case of planar inputs the first FPT algorithm was found only recently by Golovach et al. [SODA 2020]. For this case we improve upon the algorithm of Golovach et al. [SODA 2020] by designing an FPT algorithm with explicit dependence on k and hg.
AB - In the Topological Minor Deletion (TM-Deletion) problem, the input consists of an undirected graph G, a family of undirected graphs F and an integer k. The task is to determine whether G contains a set of vertices S of size at most k, such that the graph Gg- S obtained from G by removing the vertices of S, contains no graph from F as a topological minor. We give an algorithm forTM-Deletion with running time f(hg,k)· |V(G)|4. Here hg is the maximum size of a graph in F and f is a computable function of hg and k. This is the first fixed parameter tractable algorithm (FPT) for the problem. In fact, even for the restricted case of planar inputs the first FPT algorithm was found only recently by Golovach et al. [SODA 2020]. For this case we improve upon the algorithm of Golovach et al. [SODA 2020] by designing an FPT algorithm with explicit dependence on k and hg.
KW - Parameterized Complexity
KW - Topological Minor Containment
KW - Topological Minor Deletion
UR - http://www.scopus.com/inward/record.url?scp=85086760101&partnerID=8YFLogxK
U2 - 10.1145/3357713.3384318
DO - 10.1145/3357713.3384318
M3 - Conference contribution
AN - SCOPUS:85086760101
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 1317
EP - 1326
BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
A2 - Makarychev, Konstantin
A2 - Makarychev, Yury
A2 - Tulsiani, Madhur
A2 - Kamath, Gautam
A2 - Chuzhoy, Julia
PB - Association for Computing Machinery
T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Y2 - 22 June 2020 through 26 June 2020
ER -