Exact Algorithms for Edge Deletion to Cactus
Sheikh Shakil Akhtar, Geevarghese Philip
TL;DR
This paper presents improved exact algorithms for the NP-hard problem of transforming a graph into a cactus by edge deletion, and provides a polynomial-time solution for a related spanning tree problem.
Contribution
It introduces more efficient algorithms for Edge Deletion to Cactus and a polynomial-time algorithm for Spanning Tree to Cactus, advancing the understanding of these problems.
Findings
Improved exact algorithms for Edge Deletion to Cactus.
Polynomial-time algorithm for Spanning Tree to Cactus.
Edge Deletion to Cactus is NP-hard on general graphs.
Abstract
We study two related problems on simple, un-directed graphs: Edge Deletion to Cactus and Spanning Tree to Cactus. Edge Deletion to Cactus has been known to be NP-hard on general graphs at least since 1988. We show improved exact algorithms for the former and a polynomial time algorithm for the latter.
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