Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks

This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem whi...

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Bibliographic Details
Published in:European journal of operational research Vol. 316; no. 2; pp. 519 - 538
Main Authors: Ponce, Diego, Puerto, Justo, Temprano, Francisco
Format: Journal Article
Language:English
Published: Elsevier B.V 16.07.2024
Subjects:
Community detection
Complex networks
Image segmentation
Mathematical programming
Normalized cuts
Image segmentation
90C30
91C20
90C35
05C82
Complex networks
Community detection
90C27
Normalized cuts
Mathematical programming
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate large-scale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology. •MILP formulations for the k-way normalized cut problem in complex networks.•A branch-and-price algorithm for this problem which scales better.•A heuristic algorithm that provides good quality solutions for large scale problems.•Extensive computational experiments to compare the different algorithms.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2024.02.033