An Exact Algorithm for finding Maximum Induced Matching in Subcubic Graphs

TL;DR

This paper presents an exact exponential-time algorithm with improved efficiency for finding maximum induced matchings in subcubic graphs, reducing the time complexity compared to previous methods.

Contribution

It introduces a novel $O(1.2630^n)$ time algorithm for maximum induced matching in subcubic graphs, improving upon prior polynomial-space solutions.

Findings

New algorithm runs in $O(1.2630^n)$ time

Reduces computational complexity compared to previous methods

Operates within polynomial space constraints

Abstract

The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this paper, we design an exact algorithm running in $O(1.2630^n)$ time and polynomial space to solve the Maximum Induced Matching problem for graphs where each vertex has degree at most 3. Prior work solved the problem by finding the Maximum Independent Set using polynomial space in the line graph $L(G^2)$; this method uses $O(1.3139^n)$ time.