A Framework for Parameterized Subexponential Algorithms for Generalized Cycle Hitting Problems on Planar Graphs

by   Dániel Marx, et al.

Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining n^O(√(k)) time algorithms for a family of graph modification problems that includes problems that can be seen as generalized cycle hitting problems. Our starting point is the Node Unique Label Cover problem (that is, given a CSP instance where each constraint is a permutation of values on two variables, the task is to delete k variables to make the instance satisfiable). We introduce a variant of the problem where k vertices have to be deleted such that every 2-connected component of the remaining instance is satisfiable. Then we extend the problem with cardinality constraints that restrict the number of times a certain value can be used (globally or within a 2-connected component of the solution). We show that there is an n^O(√(k)) time algorithm on planar graphs for any problem that can be formulated this way, which includes a large number of well-studied problems, for example, Odd Cycle Transversal, Subset Feedback Vertex Set, Group Feedback Vertex Set, Subset Group Feedback Vertex Set, Vertex Multiway Cut, and Component Order Connectivity. For those problems that admit appropriate (quasi)polynomial kernels (that increase the parameter only linearly and preserve planarity), our results immediately imply 2^O(√(k)·polylog(k))n^O(1) time parameterized algorithms on planar graphs. In particular, we use or adapt known kernelization results to obtain 2^O(√(k)·polylog(k)) n^O(1) time (randomized) algorithms for Vertex Multiway Cut, Group Feedback Vertex Set, and Subset Feedback Vertex Set.



There are no comments yet.


page 1

page 2

page 3

page 4


Subexponential Parameterized Algorithms for Cut and Cycle Hitting Problems on H-Minor-Free Graphs

We design the first subexponential-time (parameterized) algorithms for s...

A deterministic polynomial kernel for Odd Cycle Transversal and Vertex Multiway Cut in planar graphs

We show that Odd Cycle Transversal and Vertex Multiway Cut admit determi...

Close relatives of Feedback Vertex Set without single-exponential algorithms parameterized by treewidth

The Cut Count technique and the rank-based approach have lead to sin...

Covering Many (or Few) Edges with k Vertices in Sparse Graphs

We study the following two fixed-cardinality optimization problems (a ma...

Decomposition of Map Graphs with Applications

Bidimensionality is the most common technique to design subexponential-t...

Subset Feedback Vertex Set in Chordal and Split Graphs

In the Subset Feedback Vertex Set (Subset-FVS) problem the input is a gr...

Two novel results on the existence of 3-kernels in digraphs

Let D be a digraph. We call a subset N of V(D)k-independent if for every...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.