Hitting topological minors is FPT

Fedor V. Fomin; Daniel Lokshtanov; Fahad Panolan; Saket Saurabh; Meirav Zehavi

doi:10.1145/3357713.3384318

Hitting topological minors is FPT

Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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(h^g,k)· |V(G)|⁴. Here h^g is the maximum size of a graph in F and f is a computable function of h^g 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 h^g.

Original language	American English
Title of host publication	STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Konstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
Pages	1317-1326
Number of pages	10
ISBN (Electronic)	9781450369794
DOIs	https://doi.org/10.1145/3357713.3384318
State	Published - 8 Jun 2020

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing

Keywords

Parameterized Complexity
Topological Minor Containment
Topological Minor Deletion

All Science Journal Classification (ASJC) codes

Software

Access to Document

10.1145/3357713.3384318

Cite this

Fomin, F. V., Lokshtanov, D., Panolan, F., Saurabh, S., & Zehavi, M. (2020). Hitting topological minors is FPT. In K. Makarychev, Y. Makarychev, M. Tulsiani, G. Kamath, & J. Chuzhoy (Eds.), STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing (pp. 1317-1326). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/3357713.3384318

Fomin, Fedor V. ; Lokshtanov, Daniel ; Panolan, Fahad et al. / Hitting topological minors is FPT. STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing. editor / Konstantin Makarychev ; Yury Makarychev ; Madhur Tulsiani ; Gautam Kamath ; Julia Chuzhoy. 2020. pp. 1317-1326 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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title = "Hitting topological minors is FPT",

abstract = "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.",

keywords = "Parameterized Complexity, Topological Minor Containment, Topological Minor Deletion",

author = "Fomin, {Fedor V.} and Daniel Lokshtanov and Fahad Panolan and Saket Saurabh and Meirav Zehavi",

note = "Publisher Copyright: {\textcopyright} 2020 ACM.",

year = "2020",

month = jun,

day = "8",

doi = "10.1145/3357713.3384318",

language = "American English",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

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}

Fomin, FV, Lokshtanov, D, Panolan, F, Saurabh, S & Zehavi, M 2020, Hitting topological minors is FPT. in K Makarychev, Y Makarychev, M Tulsiani, G Kamath & J Chuzhoy (eds), STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 1317-1326. https://doi.org/10.1145/3357713.3384318

Hitting topological minors is FPT. / Fomin, Fedor V.; Lokshtanov, Daniel; Panolan, Fahad et al.
STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Konstantin Makarychev; Yury Makarychev; Madhur Tulsiani; Gautam Kamath; Julia Chuzhoy. 2020. p. 1317-1326 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Hitting topological minors is FPT

AU - Fomin, Fedor V.

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

AU - Zehavi, Meirav

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

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DO - 10.1145/3357713.3384318

M3 - Conference contribution

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

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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

ER -

Hitting topological minors is FPT

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