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 -