Solving the r-pseudoforest Deletion Problem in Time Independent of r

TL;DR

This paper presents a fixed-parameter tractable algorithm for the r-pseudoforest deletion problem that operates in time independent of r, improving computational efficiency over previous methods.

Contribution

The authors develop an FPT algorithm for r-pseudoforest deletion with runtime independent of r, surpassing the double exponential dependency of prior algorithms.

Findings

Algorithm runs in O*((10k)^k) time

Runtime is independent of r, unlike previous algorithms

Provides a more efficient solution for large r values

Abstract

The feedback vertex set problem is one of the most studied parameterized problems. Several generalizations of the problem have been studied where one is to delete vertices to obtain graphs close to acyclic. In this paper, we give an FPT algorithm for the problem of deleting at most $k$ vertices to get an $r$-pseudoforest. A graph is an $r$-pseudoforest if we can delete at most $r$ edges from each component to get a forest. Philip et al. introduced this problem and gave an $O^*(c_{r}^{k})$ algorithm for it, where $c_r$ depends on $r$ double exponentially. In comparison, our algorithm runs in time $O^*((10k)^{k})$, independent of $r$.