Spanning Trees Minimizing Branching Costs
Luisa Gargano, Adele A. Rescigno

TL;DR
This paper proves that finding spanning trees with minimal branch vertices or branch costs is fixed-parameter tractable when parameterized by modular-width or neighborhood diversity, respectively, advancing the understanding of this NP-hard problem.
Contribution
It establishes fixed-parameter tractability results for the Minimum Branch Vertices Spanning Tree problem based on modular-width and neighborhood diversity parameters.
Findings
FPT algorithm for minimum branch vertices with respect to modular-width
FPT algorithm for minimum branch cost with respect to neighborhood diversity
Advances understanding of the problem's complexity in parameterized terms
Abstract
The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree in a given graph with the fewest branch vertices, defined as vertices with a degree three or more in . This problem, known to be NP-hard, has attracted significant attention due to its importance in network design and optimization. Extensive research has been conducted on the algorithmic and combinatorial aspects of this problem, with recent studies delving into its fixed-parameter tractability. In this paper, we focus primarily on the parameter modular-width. We demonstrate that finding a spanning tree with the minimum number of branch vertices is Fixed-Parameter Tractable (FPT) when considered with respect to modular-width. Additionally, in cases where each vertex in the input graph has an associated cost for serving as a branch vertex, we prove that the problem of finding a spanning tree with…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Optimization and Search Problems
