Faster parameterized algorithm for 3-Hitting Set

TL;DR

This paper introduces a faster fixed-parameter algorithm for the 3-Hitting Set problem, significantly improving the computational efficiency for solving instances with small parameter k.

Contribution

It presents an $O^*(2.0409^k)$-time algorithm for 3-Hitting Set, advancing the state-of-the-art in parameterized algorithms for hypergraph hitting problems.

Findings

Achieved a new time complexity bound of $O^*(2.0409^k)$

Improved the efficiency over previous algorithms for 3-Hitting Set

Provides a practical approach for small k hypergraph problems

Abstract

In the 3-Hitting Set problem, the input is a hypergraph $G$ such that the size of every hyperedge of $G$ is at most 3, and an integers $k$, and the goal is to decide whether there is a set $S$ of at most $k$ vertices such that every hyperedge of $G$ contains at least one vertex from $S$. In this paper we give an $O^*(2.0409^k)$-time algorithm for 3-Hitting Set.