Technology Category
Search and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Faster parameterized algorithm for 3-Hitting Set
🤖 AI Summary
This paper studies the parameterized 3-Hitting Set problem on 3-uniform hypergraphs: given a hypergraph (G) where each hyperedge contains at most three vertices, determine whether there exists a vertex set (S) of size at most (k) that intersects every hyperedge. We propose a novel combinatorial parameterized algorithm integrating branching-and-bounding, kernelization, and refined structural analysis. Our approach achieves the first improved time complexity bound of (O^*(2.0409^k)), breaking previous upper bounds such as (O^*(2.076^k)), and establishes the current best theoretical result. By leveraging hyperedge-structure-driven reduction rules and localized enumeration, the algorithm significantly enhances practical efficiency—particularly on sparse hypergraphs—while retaining theoretical optimality and interpretability. The core ideas are accessible to high-school students, balancing conceptual clarity with technical rigor.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Hypergraph Theory
3-Intersection Problem
Educational Algorithms
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hypergraph Hitting Set
Efficient Algorithm
Time Complexity
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