Interval Deletion is Fixed-Parameter Tractable

TL;DR

This paper proves that the minimum interval deletion problem, which involves removing vertices to transform a graph into an interval graph, is fixed-parameter tractable with an efficient algorithm.

Contribution

The authors develop a fixed-parameter algorithm with runtime $10^k imes n^{O(1)}$ for the interval deletion problem, establishing its fixed-parameter tractability.

Findings

The problem is fixed-parameter tractable.

The algorithm runs in $10^k imes n^{O(1)}$ time.

This advances understanding of graph modification problems.

Abstract

We study the minimum \emph{interval deletion} problem, which asks for the removal of a set of at most $k$ vertices to make a graph of $n$ vertices into an interval graph. We present a parameterized algorithm of runtime $10^k \cdot n^{O(1)}$ for this problem, that is, we show the problem is fixed-parameter tractable.