Parameterized Algorithms for Spanning Tree Isomorphism by Redundant Set Size

TL;DR

This paper develops fixed-parameter tractability algorithms for the Spanning Tree Isomorphism Problem, parameterized by the size of a redundant set, providing efficient solutions for both undirected and directed cases.

Contribution

The paper introduces new fixed-parameter algorithms for the Spanning Tree Isomorphism Problem based on redundant set size, with improved complexities for directed graphs.

Findings

Undirected algorithm runs in $O(n^2 \log n imes 2^{k \log k})$ time.

Directed algorithm runs in $O(n^2 imes 2^{4k-3})$ time.

Algorithms are fixed-parameter tractable with respect to redundant set size.

Abstract

In this paper, we present fixed-parameter tractability algorithms for both the undirected and directed versions of the Spanning Tree Isomorphism Problem, parameterized by the size $k$ of a redundant set. A redundant set is a collection of edges whose removal transforms the graph into a spanning tree. For the undirected version, our algorithm achieves a time complexity of $O(n^2 \log n \cdot 2^{k \log k})$. For the directed version, we propose a more efficient algorithm with a time complexity of $O(n^2 \cdot 2^{4k-3})$, where $n$ is the number of vertices.