A tight approximation algorithm for the cluster vertex deletion problem

We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the manag...

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Vydané v:Mathematical programming Ročník 197; číslo 2; s. 1069 - 1091
Hlavní autori: Aprile, Manuel, Drescher, Matthew, Fiorini, Samuel, Huynh, Tony
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2023
Springer
Predmet:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Twins
Sherali-Adams hierarchy
Linear programming relaxation
Approximation algorithm
Cluster vertex deletion
ISSN:0025-5610, 1436-4646
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Abstract We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the management of twins, with a novel construction of a “good” cost function on the vertices at distance at most 2 from any vertex of the input graph. As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem.
AbstractList We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the management of twins, with a novel construction of a "good" cost function on the vertices at distance at most 2 from any vertex of the input graph. As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem.
Audience Academic
Author Fiorini, Samuel
Huynh, Tony
Aprile, Manuel
Drescher, Matthew
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  organization: School of Mathematics, Monash University
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CitedBy_id crossref_primary_10_1016_j_cosrev_2025_100784
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Issue 2
Keywords Sherali-Adams hierarchy
Linear programming relaxation
Approximation algorithm
Cluster vertex deletion
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Snippet We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within...
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SubjectTerms Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
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Title A tight approximation algorithm for the cluster vertex deletion problem
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