A Polynomial Kernel for Funnel Arc Deletion Set

In Directed Feedback Arc Set ( DFAS ) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider C - Arc Deletion Set ( C - ADS ), a variant of D...

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Bibliographic Details
Published in:Algorithmica Vol. 84; no. 8; pp. 2358 - 2378
Main Author: Garlet Milani, Marcelo
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2022
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Deletion
Funnels
Graph theory
Kernels
Mathematics of Computing
Polynomials
Special Issue: Parameterized and Exact Computation (IPEC 2020)
Theory of Computation
Graph editing
Kernels
Funnels
Parameterized algorithm
Directed feedback arc set
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:In Directed Feedback Arc Set ( DFAS ) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider C - Arc Deletion Set ( C - ADS ), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class C . In this work, we choose C to be the class of funnels . Funnel - ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k . So far no polynomial kernels for this problem were known. Our main result is a kernel for Funnel - ADS with O ( k 6 ) many vertices and O ( k 7 ) many arcs, computable in O ( n m ) time, where n is the number of vertices and m the number of arcs in the input digraph.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00960-w