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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Bibliographic Details
Published in:Mathematical programming Vol. 197; no. 2; pp. 1069 - 1091
Main Authors: Aprile, Manuel, Drescher, Matthew, Fiorini, Samuel, Huynh, Tony
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2023
Springer
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01744-w