Problem
Research questions and friction points this paper is trying to address.
Edge Deletion
Cactus Graph
NP-hard
Graph Modification
Simple Undirected Graph
Exact Algorithms for Edge Deletion to Cactus
🤖 AI Summary
This work addresses two graph modification problems related to cactus graphs—graphs in which any two simple cycles share at most one vertex. The first problem, edge deletion to a cactus graph, is known to be NP-hard; the second, transforming a spanning tree into a cactus graph, has not been previously studied from an algorithmic perspective. Through careful structural analysis of graphs, the design of parameterized algorithms, and combinatorial optimization techniques, this paper presents the first polynomial-time algorithm for the spanning tree to cactus transformation problem. Furthermore, it substantially improves the exact algorithm for the edge deletion problem, yielding the fastest known method to date for solving this NP-hard task.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Edge Deletion to Cactus
Spanning Tree to Cactus
exact algorithms
polynomial time algorithm
NP-hard
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