TL;DR
This paper introduces a polynomial-time algorithm for solving the cluster vertex deletion problem specifically on chordal graphs, addressing an open research question.
Contribution
It develops a dynamic programming approach over clique trees and reduces the problem to submodular function minimization, providing a novel solution for chordal graphs.
Findings
The algorithm operates in polynomial time.
It resolves an open problem in graph modification.
Uses submodular function minimization for efficiency.
Abstract
We present a polynomial-time algorithm for the cluster vertex deletion problem on chordal graphs, resolving an open question posed in different contexts by Cao et al. [Theoretical Computer Science, 2018], Aprile et al. [Mathematical Programming, 2023], Chakraborty et al. [Discrete Applied Mathematics, 2024], and Hsieh et al. [Algorithmica, 2024]. We use dynamic programming over clique trees and reduce the computation of the optimal subproblem value to the minimization of a submodular set function.
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